diff --git a/aiohttp/web_ws.py b/aiohttp/web_ws.py
index a21443dff1b..4edc54ba31b 100644
--- a/aiohttp/web_ws.py
+++ b/aiohttp/web_ws.py
@@ -382,7 +382,10 @@ async def write_eof(self) -> None:  # type: ignore[override]
         await self.close()
         self._eof_sent = True
 
-    async def close(self, *, code: int = WSCloseCode.OK, message: bytes = b"") -> bool:
+    async def close(
+        self, *, code: int = WSCloseCode.OK, message: bytes = b"", drain: bool = True
+    ) -> bool:
+        """Close websocket connection."""
         if self._writer is None:
             raise RuntimeError("Call .prepare() first")
 
@@ -396,46 +399,52 @@ async def close(self, *, code: int = WSCloseCode.OK, message: bytes = b"") -> bo
             reader.feed_data(WS_CLOSING_MESSAGE, 0)
             await self._waiting
 
-        if not self._closed:
-            self._closed = True
-            try:
-                await self._writer.close(code, message)
-                writer = self._payload_writer
-                assert writer is not None
-                await writer.drain()
-            except (asyncio.CancelledError, asyncio.TimeoutError):
-                self._close_code = WSCloseCode.ABNORMAL_CLOSURE
-                raise
-            except Exception as exc:
-                self._close_code = WSCloseCode.ABNORMAL_CLOSURE
-                self._exception = exc
-                return True
+        if self._closed:
+            return False
 
-            if self._closing:
-                return True
+        self._closed = True
+        try:
+            await self._writer.close(code, message)
+            writer = self._payload_writer
+            assert writer is not None
+            if drain:
+                await writer.drain()
+        except (asyncio.CancelledError, asyncio.TimeoutError):
+            self._set_code_close_transport(WSCloseCode.ABNORMAL_CLOSURE)
+            raise
+        except Exception as exc:
+            self._exception = exc
+            self._set_code_close_transport(WSCloseCode.ABNORMAL_CLOSURE)
+            return True
 
-            reader = self._reader
-            assert reader is not None
-            try:
-                async with async_timeout.timeout(self._timeout):
-                    msg = await reader.read()
-            except asyncio.CancelledError:
-                self._close_code = WSCloseCode.ABNORMAL_CLOSURE
-                raise
-            except Exception as exc:
-                self._close_code = WSCloseCode.ABNORMAL_CLOSURE
-                self._exception = exc
-                return True
+        if self._closing:
+            return True
 
-            if msg.type == WSMsgType.CLOSE:
-                self._close_code = msg.data
-                return True
+        reader = self._reader
+        assert reader is not None
+        try:
+            async with async_timeout.timeout(self._timeout):
+                msg = await reader.read()
+        except asyncio.CancelledError:
+            self._set_code_close_transport(WSCloseCode.ABNORMAL_CLOSURE)
+            raise
+        except Exception as exc:
+            self._exception = exc
+            self._set_code_close_transport(WSCloseCode.ABNORMAL_CLOSURE)
+            return True
 
-            self._close_code = WSCloseCode.ABNORMAL_CLOSURE
-            self._exception = asyncio.TimeoutError()
+        if msg.type == WSMsgType.CLOSE:
+            self._set_code_close_transport(msg.data)
             return True
-        else:
-            return False
+
+        self._set_code_close_transport(WSCloseCode.ABNORMAL_CLOSURE)
+        self._exception = asyncio.TimeoutError()
+        return True
+
+    def _set_code_close_transport(self, code: WSCloseCode) -> None:
+        """Set the close code and close the transport."""
+        self._close_code = code
+        self._writer.transport.close()
 
     async def receive(self, timeout: Optional[float] = None) -> WSMessage:
         if self._reader is None:
@@ -488,7 +497,11 @@ async def receive(self, timeout: Optional[float] = None) -> WSMessage:
                 self._close_code = msg.data
                 # Could be closed while awaiting reader.
                 if not self._closed and self._autoclose:  # type: ignore[redundant-expr]
-                    await self.close()
+                    # The client is going to close the connection
+                    # out from under us so we do not want to drain
+                    # any pending writes as it will likely result
+                    # writing to a broken pipe.
+                    await self.close(drain=False)
             elif msg.type == WSMsgType.CLOSING:
                 self._closing = True
             elif msg.type == WSMsgType.PING and self._autoping: