diff --git a/package.json b/package.json
index 15c310c2ce..30254ed78d 100644
--- a/package.json
+++ b/package.json
@@ -77,6 +77,7 @@
     "highlight.js": "^10.5.0",
     "html-entities": "^1.4.0",
     "is-ip": "^3.1.0",
+    "jszip": "^3.7.0",
     "katex": "^0.12.0",
     "linkifyjs": "^2.1.9",
     "lodash": "^4.17.20",
@@ -99,10 +100,8 @@
     "resize-observer-polyfill": "^1.5.1",
     "rfc4648": "^1.4.0",
     "sanitize-html": "^2.3.2",
-    "streamsaver": "^2.0.5",
     "tar-js": "^0.3.0",
     "url": "^0.11.0",
-    "web-streams-polyfill": "^3.0.3",
     "what-input": "^5.2.10",
     "zxcvbn": "^4.4.2"
   },
@@ -131,6 +130,7 @@
     "@types/counterpart": "^0.18.1",
     "@types/css-font-loading-module": "^0.0.6",
     "@types/diff-match-patch": "^1.0.32",
+    "@types/file-saver": "^2.0.3",
     "@types/flux": "^3.1.9",
     "@types/jest": "^26.0.20",
     "@types/linkifyjs": "^2.1.3",
diff --git a/src/utils/exportUtils/Exporter.ts b/src/utils/exportUtils/Exporter.ts
index d43f937c7b..c840731d47 100644
--- a/src/utils/exportUtils/Exporter.ts
+++ b/src/utils/exportUtils/Exporter.ts
@@ -1,4 +1,3 @@
-import streamSaver from "streamsaver";
 import { MatrixEvent } from "matrix-js-sdk/src/models/event";
 import { Room } from "matrix-js-sdk/src/models/room";
 import { MatrixClientPeg } from "../../MatrixClientPeg";
@@ -7,21 +6,18 @@ import { decryptFile } from "../DecryptFile";
 import { mediaFromContent } from "../../customisations/Media";
 import { formatFullDateNoDay } from "../../DateUtils";
 import { Direction, MatrixClient } from "matrix-js-sdk";
-import streamToZIP from "./ZipStream";
-import * as ponyfill from "web-streams-polyfill/ponyfill";
-import "web-streams-polyfill/ponyfill"; // to support streams API for older browsers
 import { MutableRefObject } from "react";
+import JSZip from "jszip";
+import { saveAs } from "file-saver";
 
-type FileStream = {
+type BlobFile = {
     name: string;
-    stream(): ReadableStream;
+    blob: Blob;
 };
 
 export default abstract class Exporter {
-    protected files: FileStream[];
+    protected files: BlobFile[];
     protected client: MatrixClient;
-    protected writer: WritableStreamDefaultWriter<any>;
-    protected fileStream: WritableStream<any>;
     protected cancelled: boolean;
 
     protected constructor(
@@ -34,7 +30,6 @@ export default abstract class Exporter {
         this.files = [];
         this.client = MatrixClientPeg.get();
         window.addEventListener("beforeunload", this.onBeforeUnload);
-        window.addEventListener("onunload", this.abortWriter);
     }
 
     protected onBeforeUnload(e: BeforeUnloadEvent): string {
@@ -50,7 +45,7 @@ export default abstract class Exporter {
     protected addFile(filePath: string, blob: Blob): void {
         const file = {
             name: filePath,
-            stream: () => blob.stream(),
+            blob,
         };
         this.files.push(file);
     }
@@ -58,67 +53,31 @@ export default abstract class Exporter {
     protected async downloadZIP(): Promise<any> {
         const filename = `matrix-export-${formatFullDateNoDay(new Date())}.zip`;
 
-        // Support for older browsers
-        streamSaver.WritableStream = ponyfill.WritableStream;
-
+        const zip = new JSZip();
         // Create a writable stream to the directory
-        this.fileStream = streamSaver.createWriteStream(filename);
-
         if (!this.cancelled) this.updateProgress("Generating a ZIP");
         else return this.cleanUp();
 
-        this.writer = this.fileStream.getWriter();
-        const files = this.files;
+        for (const file of this.files) zip.file(file.name, file.blob);
 
-        const readableZipStream = streamToZIP({
-            start(ctrl) {
-                for (const file of files) ctrl.enqueue(file);
-                ctrl.close();
-            },
-        });
+        const content = await zip.generateAsync({ type: "blob" });
 
-        if (this.cancelled) return this.cleanUp();
-
-        this.updateProgress("Writing to the file system");
-
-        const reader = readableZipStream.getReader();
-        await this.pumpToFileStream(reader);
+        await saveAs(content, filename);
     }
 
     protected cleanUp(): string {
         console.log("Cleaning up...");
         window.removeEventListener("beforeunload", this.onBeforeUnload);
-        window.removeEventListener("onunload", this.abortWriter);
         return "";
     }
 
     public async cancelExport(): Promise<void> {
         console.log("Cancelling export...");
         this.cancelled = true;
-        await this.abortWriter();
     }
 
     protected async downloadPlainText(fileName: string, text: string): Promise<any> {
-        this.fileStream = streamSaver.createWriteStream(fileName);
-        this.writer = this.fileStream.getWriter();
-        const data = new TextEncoder().encode(text);
-        if (this.cancelled) return this.cleanUp();
-        await this.writer.write(data);
-        await this.writer.close();
-    }
-
-    protected async abortWriter(): Promise<void> {
-        await this.fileStream?.abort();
-        await this.writer?.abort();
-    }
-
-    protected async pumpToFileStream(reader: ReadableStreamDefaultReader): Promise<void> {
-        const res = await reader.read();
-        if (res.done) await this.writer.close();
-        else {
-            await this.writer.write(res.value);
-            await this.pumpToFileStream(reader);
-        }
+        await saveAs(new Blob[text], fileName);
     }
 
     protected setEventMetadata(event: MatrixEvent): MatrixEvent {
diff --git a/src/utils/exportUtils/ZipStream.ts b/src/utils/exportUtils/ZipStream.ts
deleted file mode 100644
index 2ee355f09c..0000000000
--- a/src/utils/exportUtils/ZipStream.ts
+++ /dev/null
@@ -1,279 +0,0 @@
-// Based on https://github.com/jimmywarting/StreamSaver.js/blob/master/examples/zip-stream.js
-
-/* global ReadableStream */
-
-type TypedArray =
-    | Int8Array
-    | Uint8Array
-    | Int16Array
-    | Uint16Array
-    | Int32Array
-    | Uint32Array
-    | Uint8ClampedArray
-    | Float32Array
-    | Float64Array;
-
-/**
- * 32-bit cyclic redundancy check, or CRC-32 - checksum
- */
-class Crc32 {
-    crc: number;
-    table: any;
-    constructor() {
-        this.crc = -1;
-        this.table = (() => {
-            let i;
-            let j;
-            let t;
-            const table = [];
-
-            for (i = 0; i < 256; i++) {
-                t = i;
-                for (j = 0; j < 8; j++) {
-                    t = (t & 1)
-                        ? (t >>> 1) ^ 0xEDB88320
-                        : t >>> 1;
-                }
-                table[i] = t;
-            }
-            return table;
-        })();
-    }
-
-    append(data: TypedArray) {
-        let crc = this.crc | 0;
-        const table = this.table;
-        for (let offset = 0, len = data.length | 0; offset < len; offset++) {
-            crc = (crc >>> 8) ^ table[(crc ^ data[offset]) & 0xFF];
-        }
-        this.crc = crc;
-    }
-
-    get() {
-        return ~this.crc;
-    }
-}
-
-type DataHelper = {
-    array: Uint8Array;
-    view: DataView;
-};
-
-const getDataHelper = (byteLength: number): DataHelper => {
-    const uint8 = new Uint8Array(byteLength);
-    return {
-        array: uint8,
-        view: new DataView(uint8.buffer),
-    };
-};
-
-type FileLike = File & {
-    directory: string;
-    comment: string;
-    stream(): ReadableStream;
-};
-
-type ZipObj = {
-    crc?: Crc32;
-    uncompressedLength: number;
-    compressedLength: number;
-    ctrl: ReadableStreamDefaultController;
-    writeFooter: Function;
-    writeHeader: Function;
-    reader?: ReadableStreamDefaultReader;
-    offset: number;
-    header?: DataHelper;
-    fileLike: FileLike;
-    level: number;
-    directory: boolean;
-};
-
-const pump = (zipObj: ZipObj) => zipObj.reader ? zipObj.reader.read().then(chunk => {
-    if (zipObj.crc) {
-        if (chunk.done) return zipObj.writeFooter();
-        const outputData = chunk.value;
-        zipObj.crc.append(outputData);
-        zipObj.uncompressedLength += outputData.length;
-        zipObj.compressedLength += outputData.length;
-        zipObj.ctrl.enqueue(outputData);
-    } else {
-        throw new Error('Missing zipObj.crc');
-    }
-}) : undefined;
-
-export default function streamToZIP(underlyingSource: UnderlyingSource) {
-    const files = Object.create(null);
-    const filenames: string[] = [];
-    const encoder = new TextEncoder();
-    let offset = 0;
-    let activeZipIndex = 0;
-    let ctrl: ReadableStreamDefaultController;
-    let activeZipObject: ZipObj;
-    let closed: boolean;
-
-    function next() {
-        activeZipIndex++;
-        activeZipObject = files[filenames[activeZipIndex]];
-        if (activeZipObject) processNextChunk();
-        else if (closed) closeZip();
-    }
-
-    const zipWriter: ReadableStreamDefaultController = {
-        desiredSize: null,
-
-        error(err) {
-            console.error(err);
-        },
-
-        enqueue(fileLike: FileLike) {
-            if (closed) {
-                throw new TypeError(
-                    "Cannot enqueue a chunk into a readable stream that is closed or has been requested to be closed",
-                );
-            }
-
-            let name = fileLike.name.trim();
-            const date = new Date(typeof fileLike.lastModified === 'undefined' ? Date.now() : fileLike.lastModified);
-
-            if (fileLike.directory && !name.endsWith('/')) name += '/';
-            // if file already exists, do not enqueue
-            if (files[name]) return;
-
-            const nameBuf = encoder.encode(name);
-            filenames.push(name);
-
-            const zipObject: ZipObj = files[name] = {
-                level: 0,
-                ctrl,
-                directory: !!fileLike.directory,
-                nameBuf,
-                comment: encoder.encode(fileLike.comment || ''),
-                compressedLength: 0,
-                uncompressedLength: 0,
-                offset,
-
-                writeHeader() {
-                    const header = getDataHelper(26);
-                    const data = getDataHelper(30 + nameBuf.length);
-
-                    zipObject.offset = offset;
-                    zipObject.header = header;
-
-                    if (zipObject.level !== 0 && !zipObject.directory) {
-                        header.view.setUint16(4, 0x0800);
-                    }
-
-                    header.view.setUint32(0, 0x14000808);
-                    header.view.setUint16(
-                        6,
-                        (((date.getHours() << 6) | date.getMinutes()) << 5) | (date.getSeconds() / 2),
-                        true,
-                    );
-                    header.view.setUint16(
-                        8,
-                        ((((date.getFullYear() - 1980) << 4) | (date.getMonth() + 1)) << 5) |
-                        date.getDate(),
-                        true,
-                    );
-                    header.view.setUint16(22, nameBuf.length, true);
-                    data.view.setUint32(0, 0x504b0304);
-                    data.array.set(header.array, 4);
-                    data.array.set(nameBuf, 30);
-                    offset += data.array.length;
-                    ctrl.enqueue(data.array);
-                },
-
-                writeFooter() {
-                    const footer = getDataHelper(16);
-                    footer.view.setUint32(0, 0x504b0708);
-
-                    if (zipObject.crc && zipObject.header) {
-                        zipObject.header.view.setUint32(10, zipObject.crc.get(), true);
-                        zipObject.header.view.setUint32(14, zipObject.compressedLength, true);
-                        zipObject.header.view.setUint32(18, zipObject.uncompressedLength, true);
-                        footer.view.setUint32(4, zipObject.crc.get(), true);
-                        footer.view.setUint32(8, zipObject.compressedLength, true);
-                        footer.view.setUint32(12, zipObject.uncompressedLength, true);
-                    }
-
-                    ctrl.enqueue(footer.array);
-                    offset += zipObject.compressedLength + 16;
-                    next();
-                },
-                fileLike,
-            };
-
-            if (!activeZipObject) {
-                activeZipObject = zipObject;
-                processNextChunk();
-            }
-        },
-
-        close() {
-            if (closed) {
-                throw new TypeError(
-                    "Cannot close a readable stream that has already been requested to be closed",
-                );
-            }
-            if (!activeZipObject) closeZip();
-            closed = true;
-        },
-    };
-
-    function closeZip() {
-        let length = 0;
-        let index = 0;
-        let indexFilename: number;
-        let file: any;
-
-        for (indexFilename = 0; indexFilename < filenames.length; indexFilename++) {
-            file = files[filenames[indexFilename]];
-            length += 46 + file.nameBuf.length + file.comment.length;
-        }
-        const data = getDataHelper(length + 22);
-        for (indexFilename = 0; indexFilename < filenames.length; indexFilename++) {
-            file = files[filenames[indexFilename]];
-            data.view.setUint32(index, 0x504b0102);
-            data.view.setUint16(index + 4, 0x1400);
-            data.array.set(file.header.array, index + 6);
-            data.view.setUint16(index + 32, file.comment.length, true);
-            if (file.directory) {
-                data.view.setUint8(index + 38, 0x10);
-            }
-            data.view.setUint32(index + 42, file.offset, true);
-            data.array.set(file.nameBuf, index + 46);
-            data.array.set(file.comment, index + 46 + file.nameBuf.length);
-            index += 46 + file.nameBuf.length + file.comment.length;
-        }
-        data.view.setUint32(index, 0x504b0506);
-        data.view.setUint16(index + 8, filenames.length, true);
-        data.view.setUint16(index + 10, filenames.length, true);
-        data.view.setUint32(index + 12, length, true);
-        data.view.setUint32(index + 16, offset, true);
-        ctrl.enqueue(data.array);
-        ctrl.close();
-    }
-
-    function processNextChunk() {
-        if (!activeZipObject) return;
-        if (activeZipObject.reader) return pump(activeZipObject);
-        if (activeZipObject.fileLike.stream) {
-            activeZipObject.crc = new Crc32();
-            activeZipObject.reader = activeZipObject.fileLike.stream().getReader();
-            activeZipObject.writeHeader();
-        } else next();
-    }
-
-    return new ReadableStream({
-        start: c => {
-            ctrl = c;
-            underlyingSource.start && Promise.resolve(underlyingSource.start(zipWriter));
-        },
-        pull() {
-            return processNextChunk() || (
-                underlyingSource.pull &&
-                Promise.resolve(underlyingSource.pull(zipWriter))
-            );
-        },
-    });
-}
diff --git a/yarn.lock b/yarn.lock
index 8801940a35..dc3bc2ca7b 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -1468,6 +1468,11 @@
   resolved "https://registry.yarnpkg.com/@types/fbemitter/-/fbemitter-2.0.32.tgz#8ed204da0f54e9c8eaec31b1eec91e25132d082c"
   integrity sha1-jtIE2g9U6cjq7DGx7skeJRMtCCw=
 
+"@types/file-saver@^2.0.3":
+  version "2.0.3"
+  resolved "https://registry.yarnpkg.com/@types/file-saver/-/file-saver-2.0.3.tgz#b734c4f5a04d20615eaed3dc106e2ab321082009"
+  integrity sha512-MBIou8pd/41jkff7s97B47bc9+p0BszqqDJsO51yDm49uUxeKzrfuNl5fSLC6BpLEWKA8zlwyqALVmXrFwoBHQ==
+
 "@types/flux@^3.1.9":
   version "3.1.10"
   resolved "https://registry.yarnpkg.com/@types/flux/-/flux-3.1.10.tgz#7c6306e86ecb434d00f38cb82f092640c7bd4098"
@@ -4141,6 +4146,11 @@ ignore@^5.1.4, ignore@^5.1.8:
   resolved "https://registry.yarnpkg.com/ignore/-/ignore-5.1.8.tgz#f150a8b50a34289b33e22f5889abd4d8016f0e57"
   integrity sha512-BMpfD7PpiETpBl/A6S498BaIJ6Y/ABT93ETbby2fP00v4EbvPBXWEoaR1UBPKs3iR53pJY7EtZk5KACI57i1Uw==
 
+immediate@~3.0.5:
+  version "3.0.6"
+  resolved "https://registry.yarnpkg.com/immediate/-/immediate-3.0.6.tgz#9db1dbd0faf8de6fbe0f5dd5e56bb606280de69b"
+  integrity sha1-nbHb0Pr43m++D13V5Wu2BigN5ps=
+
 immutable@^3.7.4:
   version "3.8.2"
   resolved "https://registry.yarnpkg.com/immutable/-/immutable-3.8.2.tgz#c2439951455bb39913daf281376f1530e104adf3"
@@ -5235,6 +5245,16 @@ jsprim@^1.2.2:
     array-includes "^3.1.2"
     object.assign "^4.1.2"
 
+jszip@^3.7.0:
+  version "3.7.0"
+  resolved "https://registry.yarnpkg.com/jszip/-/jszip-3.7.0.tgz#9b8b995a4e7c9024653ce743e902076a82fdf4e6"
+  integrity sha512-Y2OlFIzrDOPWUnpU0LORIcDn2xN7rC9yKffFM/7pGhQuhO+SUhfm2trkJ/S5amjFvem0Y+1EALz/MEPkvHXVNw==
+  dependencies:
+    lie "~3.3.0"
+    pako "~1.0.2"
+    readable-stream "~2.3.6"
+    set-immediate-shim "~1.0.1"
+
 katex@^0.12.0:
   version "0.12.0"
   resolved "https://registry.yarnpkg.com/katex/-/katex-0.12.0.tgz#2fb1c665dbd2b043edcf8a1f5c555f46beaa0cb9"
@@ -5302,6 +5322,13 @@ levn@~0.3.0:
     prelude-ls "~1.1.2"
     type-check "~0.3.2"
 
+lie@~3.3.0:
+  version "3.3.0"
+  resolved "https://registry.yarnpkg.com/lie/-/lie-3.3.0.tgz#dcf82dee545f46074daf200c7c1c5a08e0f40f6a"
+  integrity sha512-UaiMJzeWRlEujzAuw5LokY1L5ecNQYZKfmyZ9L7wDHb/p5etKaxXhohBcrw0EYby+G/NA52vRSN4N39dxHAIwQ==
+  dependencies:
+    immediate "~3.0.5"
+
 lines-and-columns@^1.1.6:
   version "1.1.6"
   resolved "https://registry.yarnpkg.com/lines-and-columns/-/lines-and-columns-1.1.6.tgz#1c00c743b433cd0a4e80758f7b64a57440d9ff00"
@@ -6015,6 +6042,11 @@ pako@^2.0.3:
   resolved "https://registry.yarnpkg.com/pako/-/pako-2.0.3.tgz#cdf475e31b678565251406de9e759196a0ea7a43"
   integrity sha512-WjR1hOeg+kki3ZIOjaf4b5WVcay1jaliKSYiEaB1XzwhMQZJxRdQRv0V31EKBYlxb4T7SK3hjfc/jxyU64BoSw==
 
+pako@~1.0.2:
+  version "1.0.11"
+  resolved "https://registry.yarnpkg.com/pako/-/pako-1.0.11.tgz#6c9599d340d54dfd3946380252a35705a6b992bf"
+  integrity sha512-4hLB8Py4zZce5s4yd9XzopqwVv/yGNhV1Bl8NTmCq1763HeK2+EwVTv+leGeL13Dnh2wfbqowVPXCIO0z4taYw==
+
 parent-module@^1.0.0:
   version "1.0.1"
   resolved "https://registry.yarnpkg.com/parent-module/-/parent-module-1.0.1.tgz#691d2709e78c79fae3a156622452d00762caaaa2"
@@ -6552,7 +6584,7 @@ read-pkg@^5.2.0:
     parse-json "^5.0.0"
     type-fest "^0.6.0"
 
-readable-stream@^2.0.2:
+readable-stream@^2.0.2, readable-stream@~2.3.6:
   version "2.3.7"
   resolved "https://registry.yarnpkg.com/readable-stream/-/readable-stream-2.3.7.tgz#1eca1cf711aef814c04f62252a36a62f6cb23b57"
   integrity sha512-Ebho8K4jIbHAxnuxi7o42OrZgF/ZTNcsZj6nRKyUmkhLFq8CHItp/fy6hQZuZmP/n3yZ9VBUbp4zz/mX8hmYPw==
@@ -6953,6 +6985,11 @@ set-blocking@^2.0.0:
   resolved "https://registry.yarnpkg.com/set-blocking/-/set-blocking-2.0.0.tgz#045f9782d011ae9a6803ddd382b24392b3d890f7"
   integrity sha1-BF+XgtARrppoA93TgrJDkrPYkPc=
 
+set-immediate-shim@~1.0.1:
+  version "1.0.1"
+  resolved "https://registry.yarnpkg.com/set-immediate-shim/-/set-immediate-shim-1.0.1.tgz#4b2b1b27eb808a9f8dcc481a58e5e56f599f3f61"
+  integrity sha1-SysbJ+uAip+NzEgaWOXlb1mfP2E=
+
 set-value@^2.0.0, set-value@^2.0.1:
   version "2.0.1"
   resolved "https://registry.yarnpkg.com/set-value/-/set-value-2.0.1.tgz#a18d40530e6f07de4228c7defe4227af8cad005b"
@@ -7206,11 +7243,6 @@ static-extend@^0.1.1:
     define-property "^0.2.5"
     object-copy "^0.1.0"
 
-streamsaver@^2.0.5:
-  version "2.0.5"
-  resolved "https://registry.yarnpkg.com/streamsaver/-/streamsaver-2.0.5.tgz#3212f0e908fcece5b3a65591094475cf87850d00"
-  integrity sha512-KIWtBvi8A6FiFZGNSyuIZRZM6C8AvnWTiCx/TYa7so420vC5sQwcBKkdqInuGWoWMfeWy/P+/cRqMtWVf4RW9w==
-
 string-length@^4.0.1:
   version "4.0.2"
   resolved "https://registry.yarnpkg.com/string-length/-/string-length-4.0.2.tgz#a8a8dc7bd5c1a82b9b3c8b87e125f66871b6e57a"
@@ -7916,11 +7948,6 @@ walker@^1.0.7, walker@~1.0.5:
   dependencies:
     makeerror "1.0.x"
 
-web-streams-polyfill@^3.0.3:
-  version "3.0.3"
-  resolved "https://registry.yarnpkg.com/web-streams-polyfill/-/web-streams-polyfill-3.0.3.tgz#f49e487eedeca47a207c1aee41ee5578f884b42f"
-  integrity sha512-d2H/t0eqRNM4w2WvmTdoeIvzAUSpK7JmATB8Nr2lb7nQ9BTIJVjbQ/TRFVEh2gUH1HwclPdoPtfMoFfetXaZnA==
-
 webcrypto-core@^1.2.0:
   version "1.2.0"
   resolved "https://registry.yarnpkg.com/webcrypto-core/-/webcrypto-core-1.2.0.tgz#44fda3f9315ed6effe9a1e47466e0935327733b5"