diff --git a/CHANGES/5854.bugfix b/CHANGES/5854.bugfix
new file mode 100644
index 00000000000..b7de2f4d232
--- /dev/null
+++ b/CHANGES/5854.bugfix
@@ -0,0 +1 @@
+Fixed client timeout not working when incoming data is always available without waiting -- by :user:`Dreamsorcerer`.
diff --git a/aiohttp/helpers.py b/aiohttp/helpers.py
index 4b7ce168e3b..47caeebcc93 100644
--- a/aiohttp/helpers.py
+++ b/aiohttp/helpers.py
@@ -682,7 +682,8 @@ def __call__(self) -> None:
 
 
 class BaseTimerContext(ContextManager["BaseTimerContext"]):
-    pass
+    def assert_timeout(self) -> None:
+        """Raise TimeoutError if timeout has been exceeded."""
 
 
 class TimerNoop(BaseTimerContext):
@@ -706,6 +707,11 @@ def __init__(self, loop: asyncio.AbstractEventLoop) -> None:
         self._tasks: List[asyncio.Task[Any]] = []
         self._cancelled = False
 
+    def assert_timeout(self) -> None:
+        """Raise TimeoutError if timer has already been cancelled."""
+        if self._cancelled:
+            raise asyncio.TimeoutError from None
+
     def __enter__(self) -> BaseTimerContext:
         task = current_task(loop=self._loop)
 
diff --git a/aiohttp/streams.py b/aiohttp/streams.py
index 32ec7f148f6..ea4bcd3c5a4 100644
--- a/aiohttp/streams.py
+++ b/aiohttp/streams.py
@@ -4,7 +4,7 @@
 from typing import Awaitable, Callable, Deque, Generic, List, Optional, Tuple, TypeVar
 
 from .base_protocol import BaseProtocol
-from .helpers import BaseTimerContext, set_exception, set_result
+from .helpers import BaseTimerContext, TimerNoop, set_exception, set_result
 from .log import internal_logger
 from .typedefs import Final
 
@@ -116,7 +116,7 @@ def __init__(
         self._waiter: Optional[asyncio.Future[None]] = None
         self._eof_waiter: Optional[asyncio.Future[None]] = None
         self._exception: Optional[BaseException] = None
-        self._timer = timer
+        self._timer = TimerNoop() if timer is None else timer
         self._eof_callbacks: List[Callable[[], None]] = []
 
     def __repr__(self) -> str:
@@ -291,10 +291,7 @@ async def _wait(self, func_name: str) -> None:
 
         waiter = self._waiter = self._loop.create_future()
         try:
-            if self._timer:
-                with self._timer:
-                    await waiter
-            else:
+            with self._timer:
                 await waiter
         finally:
             self._waiter = None
@@ -485,8 +482,9 @@ def _read_nowait_chunk(self, n: int) -> bytes:
 
     def _read_nowait(self, n: int) -> bytes:
         """Read not more than n bytes, or whole buffer if n == -1"""
-        chunks = []
+        self._timer.assert_timeout()
 
+        chunks = []
         while self._buffer:
             chunk = self._read_nowait_chunk(n)
             chunks.append(chunk)
diff --git a/tests/test_client_functional.py b/tests/test_client_functional.py
index 93f0dc06a14..81a80eca677 100644
--- a/tests/test_client_functional.py
+++ b/tests/test_client_functional.py
@@ -3034,6 +3034,30 @@ async def handler(request):
             await resp.read()
 
 
+async def test_timeout_with_full_buffer(aiohttp_client) -> None:
+    async def handler(request):
+        """Server response that never ends and always has more data available."""
+        resp = web.StreamResponse()
+        await resp.prepare(request)
+        while True:
+            await resp.write(b"1" * 1000)
+            await asyncio.sleep(0.01)
+
+    async def request(client):
+        timeout = aiohttp.ClientTimeout(total=0.5)
+        async with await client.get("/", timeout=timeout) as resp:
+            with pytest.raises(asyncio.TimeoutError):
+                async for data in resp.content.iter_chunked(1):
+                    await asyncio.sleep(0.01)
+
+    app = web.Application()
+    app.add_routes([web.get("/", handler)])
+
+    client = await aiohttp_client(app)
+    # wait_for() used just to ensure that a failing test doesn't hang.
+    await asyncio.wait_for(request(client), 1)
+
+
 async def test_read_bufsize_session_default(aiohttp_client) -> None:
     async def handler(request):
         return web.Response(body=b"1234567")