diff --git a/packages/playwright-core/src/server/webkit/wkPage.ts b/packages/playwright-core/src/server/webkit/wkPage.ts
index 4cb5dbdd5e3f4..e5d065f784aae 100644
--- a/packages/playwright-core/src/server/webkit/wkPage.ts
+++ b/packages/playwright-core/src/server/webkit/wkPage.ts
@@ -211,8 +211,8 @@ export class WKPage implements PageDelegate {
       }));
     }
     promises.push(session.send('Network.setExtraHTTPHeaders', { headers: headersArrayToObject(this._calculateExtraHTTPHeaders(), false /* lowerCase */) }));
-    if (contextOptions.offline)
-      promises.push(session.send('Network.setEmulateOfflineState', { offline: true }));
+    if (contextOptions.offline !== undefined)
+      promises.push(session.send('Network.setEmulateOfflineState', { offline: contextOptions.offline }));
     promises.push(session.send('Page.setTouchEmulationEnabled', { enabled: !!contextOptions.hasTouch }));
     if (contextOptions.timezoneId) {
       promises.push(session.send('Page.setTimeZone', { timeZone: contextOptions.timezoneId }).
diff --git a/tests/library/browsercontext-service-worker-policy.spec.ts b/tests/library/browsercontext-service-worker-policy.spec.ts
index 1923a2dc4e6b3..5f660269d75be 100644
--- a/tests/library/browsercontext-service-worker-policy.spec.ts
+++ b/tests/library/browsercontext-service-worker-policy.spec.ts
@@ -20,6 +20,83 @@ it('should allow service workers by default', async ({ page, server }) => {
   await expect(page.evaluate(() => window['registrationPromise'])).resolves.toBeTruthy();
 });
 
+for (const [mode, workerResponse] of Object.entries({
+  'literal': `new Response('<h1>offline</h1>', { headers: { 'Content-Type': 'text/html' } })`,
+  'cache-only': `caches.match('/offline.html')`,
+  'network-fallback': `fetch(event.request).catch(() => caches.match('/offline.html'))`,
+  'preload-fallback': `(async () => {
+    try {
+      return await event.preloadResponse || await fetch(event.request);
+    } catch {
+      return caches.match('/offline.html');
+    }
+  })()`,
+})) {
+  it(`should allow ${mode} service worker navigation while offline`, {
+    annotation: { type: 'issue', description: 'https://github.com/microsoft/playwright/issues/42775' },
+  }, async ({ context, page, server, browserName, isElectron, isFrozenWebkit }) => {
+    it.skip(isElectron);
+    it.skip(isFrozenWebkit, 'Requires offline emulation in the network process.');
+    it.fixme(browserName === 'firefox' && (mode === 'network-fallback' || mode === 'preload-fallback'), 'Firefox does not apply offline emulation to service worker requests.');
+
+    let networkRequests = 0;
+    server.setRoute('/target.html', (request, response) => {
+      ++networkRequests;
+      response.setHeader('Cache-Control', 'no-store');
+      response.end('online');
+    });
+    server.setRoute('/offline.html', (request, response) => {
+      response.setHeader('Content-Type', 'text/html');
+      response.end('<h1>offline</h1>');
+    });
+    server.setRoute('/sw.js', (request, response) => {
+      response.setHeader('Content-Type', 'application/javascript');
+      response.end(`
+        self.addEventListener('install', event => event.waitUntil((async () => {
+          const cache = await caches.open('offline');
+          await cache.add('/offline.html');
+          await self.skipWaiting();
+        })()));
+        self.addEventListener('activate', event => event.waitUntil((async () => {
+          ${mode === 'preload-fallback' ? 'await self.registration.navigationPreload.enable();' : ''}
+          await self.clients.claim();
+        })()));
+        self.addEventListener('fetch', event => {
+          if (event.request.mode === 'navigate')
+            event.respondWith(${workerResponse});
+        });
+      `);
+    });
+
+    await page.goto(server.EMPTY_PAGE);
+    await page.evaluate(async () => {
+      await navigator.serviceWorker.register('/sw.js');
+      await navigator.serviceWorker.ready;
+    });
+    await page.waitForFunction(() => !!navigator.serviceWorker.controller);
+    await context.setOffline(true);
+
+    const response = await page.goto(server.PREFIX + '/target.html');
+    expect(response.status()).toBe(200);
+    expect(response.fromServiceWorker()).toBe(true);
+    await expect(page.locator('h1')).toHaveText('offline');
+    expect(await page.evaluate(() => navigator.onLine)).toBe(false);
+    expect(networkRequests).toBe(0);
+
+    const newPage = await context.newPage();
+    const newResponse = await newPage.goto(server.PREFIX + '/target.html');
+    expect(newResponse.status()).toBe(200);
+    expect(newResponse.fromServiceWorker()).toBe(true);
+    await expect(newPage.locator('h1')).toHaveText('offline');
+    expect(await newPage.evaluate(() => navigator.onLine)).toBe(false);
+    expect(networkRequests).toBe(0);
+
+    await context.setOffline(false);
+    expect(await page.evaluate(() => fetch('/target.html').then(response => response.text()))).toBe('online');
+    expect(networkRequests).toBe(1);
+  });
+}
+
 it.describe('block', () => {
   it.use({ serviceWorkers: 'block' });