diff --git a/cypress/e2e/read-receipts/read-receipts.spec.ts b/cypress/e2e/read-receipts/read-receipts.spec.ts
new file mode 100644
index 0000000000..da84b0060f
--- /dev/null
+++ b/cypress/e2e/read-receipts/read-receipts.spec.ts
@@ -0,0 +1,133 @@
+/*
+Copyright 2023 The Matrix.org Foundation C.I.C.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/// <reference types="cypress" />
+
+import type { MatrixClient, MatrixEvent } from "matrix-js-sdk/src/matrix";
+import type { ISendEventResponse } from "matrix-js-sdk/src/@types/requests";
+import type { ReceiptType } from "matrix-js-sdk/src/@types/read_receipts";
+import { HomeserverInstance } from "../../plugins/utils/homeserver";
+
+describe("Read receipts", () => {
+    const userName = "Mae";
+    const botName = "Other User";
+    const selectedRoomName = "Selected Room";
+    const otherRoomName = "Other Room";
+
+    let homeserver: HomeserverInstance;
+    let otherRoomId: string;
+    let selectedRoomId: string;
+    let bot: MatrixClient | undefined;
+
+    const botSendMessage = (): Cypress.Chainable<ISendEventResponse> => {
+        return cy.botSendMessage(bot, otherRoomId, "Message");
+    };
+
+    const fakeEventFromSent = (eventResponse: ISendEventResponse): MatrixEvent => {
+        return {
+            getRoomId: () => otherRoomId,
+            getId: () => eventResponse.event_id,
+            threadRootId: undefined,
+            getTs: () => 1,
+        } as any as MatrixEvent;
+    };
+
+    beforeEach(() => {
+        /*
+         * Create 2 rooms:
+         *
+         * - Selected room - this one is clicked in the UI
+         * - Other room - this one contains the bot, which will send events so
+         *                we can check its unread state.
+         */
+        cy.startHomeserver("default").then((data) => {
+            homeserver = data;
+            cy.initTestUser(homeserver, userName)
+                .then(() => {
+                    cy.createRoom({ name: selectedRoomName }).then((createdRoomId) => {
+                        selectedRoomId = createdRoomId;
+                    });
+                })
+                .then(() => {
+                    cy.createRoom({ name: otherRoomName }).then((createdRoomId) => {
+                        otherRoomId = createdRoomId;
+                    });
+                })
+                .then(() => {
+                    cy.getBot(homeserver, { displayName: botName }).then((botClient) => {
+                        bot = botClient;
+                    });
+                })
+                .then(() => {
+                    // Invite the bot to Other room
+                    cy.inviteUser(otherRoomId, bot.getUserId());
+                    cy.visit("/#/room/" + otherRoomId);
+                    cy.findByText(botName + " joined the room").should("exist");
+
+                    // Then go into Selected room
+                    cy.visit("/#/room/" + selectedRoomId);
+                });
+        });
+    });
+
+    afterEach(() => {
+        cy.stopHomeserver(homeserver);
+    });
+
+    it(
+        "Considers room read if there's a receipt for main even if an earlier unthreaded receipt exists #24629",
+        {
+            // When #24629 exists, the test fails the first time but passes later, so we disable retries
+            // to be sure we are going to fail if the bug comes back.
+            // Why does it pass the second time? I wish I knew. (andyb)
+            retries: 0,
+        },
+        () => {
+            // Details are in https://github.com/vector-im/element-web/issues/24629
+            // This proves we've fixed one of the "stuck unreads" issues.
+
+            // Given we sent 3 events on the main thread
+            botSendMessage();
+            botSendMessage().then((main2) => {
+                botSendMessage().then((main3) => {
+                    // (So the room starts off unread)
+                    cy.findByLabelText(`${otherRoomName} 3 unread messages.`).should("exist");
+
+                    // When we send a threaded receipt for the last event in main
+                    // And an unthreaded receipt for an earlier event
+                    cy.sendReadReceipt(fakeEventFromSent(main3));
+                    cy.sendReadReceipt(fakeEventFromSent(main2), "m.read" as any as ReceiptType, true);
+
+                    // (So the room has no unreads)
+                    cy.findByLabelText(`${otherRoomName}`).should("exist");
+
+                    // And we persuade the app to persist its state to indexeddb by reloading and waiting
+                    cy.reload();
+                    cy.findByLabelText(`${selectedRoomName}`).should("exist");
+
+                    // And we reload again, fetching the persisted state FROM indexeddb
+                    cy.reload();
+
+                    // Then the room is read, because the persisted state correctly remembers both
+                    // receipts. (In #24629, the unthreaded receipt overwrote the main thread one,
+                    // meaning that the room still said it had unread messages.)
+                    cy.findByLabelText(`${otherRoomName}`).should("exist");
+                    cy.findByLabelText(`${otherRoomName} Unread messages.`).should("not.exist");
+                });
+            });
+        },
+    );
+});
diff --git a/cypress/support/client.ts b/cypress/support/client.ts
index 535669d6be..fca966613e 100644
--- a/cypress/support/client.ts
+++ b/cypress/support/client.ts
@@ -20,7 +20,8 @@ import type { FileType, Upload, UploadOpts } from "matrix-js-sdk/src/http-api";
 import type { ICreateRoomOpts, ISendEventResponse } from "matrix-js-sdk/src/@types/requests";
 import type { MatrixClient } from "matrix-js-sdk/src/client";
 import type { Room } from "matrix-js-sdk/src/models/room";
-import type { IContent } from "matrix-js-sdk/src/models/event";
+import type { IContent, MatrixEvent } from "matrix-js-sdk/src/models/event";
+import type { ReceiptType } from "matrix-js-sdk/src/@types/read_receipts";
 import Chainable = Cypress.Chainable;
 import { UserCredentials } from "./login";
 
@@ -69,6 +70,13 @@ declare global {
                 eventType: string,
                 content: IContent,
             ): Chainable<ISendEventResponse>;
+            /**
+             * @param {MatrixEvent} event
+             * @param {ReceiptType} receiptType
+             * @param {boolean} unthreaded
+             * @return {module:http-api.MatrixError} Rejects: with an error response.
+             */
+            sendReadReceipt(event: MatrixEvent, receiptType?: ReceiptType, unthreaded?: boolean): Chainable<{}>;
             /**
              * @param {string} name
              * @param {module:client.callback} callback Optional.
@@ -195,6 +203,15 @@ Cypress.Commands.add(
     },
 );
 
+Cypress.Commands.add(
+    "sendReadReceipt",
+    (event: MatrixEvent, receiptType?: ReceiptType, unthreaded?: boolean): Chainable<{}> => {
+        return cy.getClient().then(async (cli: MatrixClient) => {
+            return cli.sendReadReceipt(event, receiptType, unthreaded);
+        });
+    },
+);
+
 Cypress.Commands.add("setDisplayName", (name: string): Chainable<{}> => {
     return cy.getClient().then(async (cli: MatrixClient) => {
         return cli.setDisplayName(name);