diff --git a/channels/consumer.py b/channels/consumer.py
index fc065432..c241e8fd 100644
--- a/channels/consumer.py
+++ b/channels/consumer.py
@@ -47,6 +47,15 @@ async def __call__(self, scope, receive, send):
             self.channel_receive = functools.partial(
                 self.channel_layer.receive, self.channel_name
             )
+        # Handler to call when dispatch task is cancelled
+        cancel_callback = None
+        try:
+            if callable(self.channel_layer.clean_channel):
+                cancel_callback = functools.partial(
+                    self.channel_layer.clean_channel, self.channel_name
+                )
+        except AttributeError:
+            pass
         # Store send function
         if self._sync:
             self.base_send = async_to_sync(send)
@@ -56,7 +65,9 @@ async def __call__(self, scope, receive, send):
         try:
             if self.channel_layer is not None:
                 await await_many_dispatch(
-                    [receive, self.channel_receive], self.dispatch
+                    [receive, self.channel_receive],
+                    self.dispatch,
+                    cancel_callback=cancel_callback,
                 )
             else:
                 await await_many_dispatch([receive], self.dispatch)
diff --git a/channels/utils.py b/channels/utils.py
index 72cd9ca3..0478f328 100644
--- a/channels/utils.py
+++ b/channels/utils.py
@@ -29,7 +29,7 @@ def name_that_thing(thing):
     return repr(thing)
 
 
-async def await_many_dispatch(consumer_callables, dispatch):
+async def await_many_dispatch(consumer_callables, dispatch, cancel_callback=None):
     """
     Given a set of consumer callables, awaits on them all and passes results
     from them to the dispatch awaitable as they come in.
@@ -56,4 +56,5 @@ async def await_many_dispatch(consumer_callables, dispatch):
             try:
                 await task
             except asyncio.CancelledError:
-                pass
+                if cancel_callback:
+                    await cancel_callback()
diff --git a/tests/test_utils.py b/tests/test_utils.py
new file mode 100644
index 00000000..e7654da3
--- /dev/null
+++ b/tests/test_utils.py
@@ -0,0 +1,20 @@
+import asyncio
+from unittest import mock
+
+import async_timeout
+import pytest
+
+from channels.utils import await_many_dispatch
+
+
+async def sleep_task(*args):
+    await asyncio.sleep(10)
+
+
+@pytest.mark.asyncio
+async def test_cancel_callback_called():
+    cancel_callback = mock.AsyncMock()
+    with pytest.raises(asyncio.TimeoutError):
+        async with async_timeout.timeout(0):
+            await await_many_dispatch([sleep_task], sleep_task, cancel_callback)
+    assert cancel_callback.called