diff --git a/packages/playwright-core/browsers.json b/packages/playwright-core/browsers.json
index 43963417fc..1c86a1303c 100644
--- a/packages/playwright-core/browsers.json
+++ b/packages/playwright-core/browsers.json
@@ -27,7 +27,7 @@
     },
     {
       "name": "webkit",
-      "revision": "2065",
+      "revision": "2066",
       "installByDefault": true,
       "revisionOverrides": {
         "mac10.14": "1446",
diff --git a/tests/library/client-certificates.spec.ts b/tests/library/client-certificates.spec.ts
index 807af5154c..75ca2468f7 100644
--- a/tests/library/client-certificates.spec.ts
+++ b/tests/library/client-certificates.spec.ts
@@ -601,8 +601,7 @@ test.describe('browser', () => {
 
   test('support http2', async ({ browser, startCCServer, asset, browserName }) => {
     test.skip(browserName === 'webkit' && process.platform === 'darwin', 'WebKit on macOS doesn\n proxy localhost');
-    const enableHTTP1FallbackWhenUsingHttp2 = browserName === 'webkit' && process.platform === 'linux';
-    const serverURL = await startCCServer({ http2: true, enableHTTP1FallbackWhenUsingHttp2 });
+    const serverURL = await startCCServer({ http2: true });
     const page = await browser.newPage({
       ignoreHTTPSErrors: true,
       clientCertificates: [{
@@ -611,19 +610,16 @@ test.describe('browser', () => {
         keyPath: asset('client-certificates/client/trusted/key.pem'),
       }],
     });
-    // TODO: We should investigate why http2 is not supported in WebKit on Linux.
-    // https://bugs.webkit.org/show_bug.cgi?id=276990
-    const expectedProtocol = enableHTTP1FallbackWhenUsingHttp2 ? 'http/1.1' : 'h2';
     {
       await page.goto(serverURL.replace('localhost', 'local.playwright'));
       await expect(page.getByTestId('message')).toHaveText('Sorry, but you need to provide a client certificate to continue.');
-      await expect(page.getByTestId('alpn-protocol')).toHaveText(expectedProtocol);
+      await expect(page.getByTestId('alpn-protocol')).toHaveText('h2');
       await expect(page.getByTestId('servername')).toHaveText('local.playwright');
     }
     {
       await page.goto(serverURL);
       await expect(page.getByTestId('message')).toHaveText('Hello Alice, your certificate was issued by localhost!');
-      await expect(page.getByTestId('alpn-protocol')).toHaveText(expectedProtocol);
+      await expect(page.getByTestId('alpn-protocol')).toHaveText('h2');
     }
     await page.close();
   });