diff --git a/changelog.d/12708.misc b/changelog.d/12708.misc
new file mode 100644
index 000000000..aa99e7311
--- /dev/null
+++ b/changelog.d/12708.misc
@@ -0,0 +1 @@
+Enable cancellation of `GET /rooms/$room_id/members`, `GET /rooms/$room_id/state` and `GET /rooms/$room_id/state/$event_type/*` requests.
diff --git a/synapse/http/server.py b/synapse/http/server.py
index 756c6e1ae..e3dcc3f3d 100644
--- a/synapse/http/server.py
+++ b/synapse/http/server.py
@@ -139,7 +139,9 @@ def cancellable(method: F) -> F:
             async def on_GET(self, request: SynapseRequest) -> ...:
                 ...
     """
-    if method.__name__ not in _cancellable_method_names:
+    if method.__name__ not in _cancellable_method_names and not any(
+        method.__name__.startswith(prefix) for prefix in _cancellable_method_names
+    ):
         raise ValueError(
             "@cancellable decorator can only be applied to servlet methods."
         )
diff --git a/synapse/rest/client/room.py b/synapse/rest/client/room.py
index 906fe09e9..4b8bfbffc 100644
--- a/synapse/rest/client/room.py
+++ b/synapse/rest/client/room.py
@@ -34,7 +34,7 @@ from synapse.api.errors import (
 )
 from synapse.api.filtering import Filter
 from synapse.events.utils import format_event_for_client_v2
-from synapse.http.server import HttpServer
+from synapse.http.server import HttpServer, cancellable
 from synapse.http.servlet import (
     ResolveRoomIdMixin,
     RestServlet,
@@ -143,6 +143,7 @@ class RoomStateEventRestServlet(TransactionRestServlet):
             self.__class__.__name__,
         )
 
+    @cancellable
     def on_GET_no_state_key(
         self, request: SynapseRequest, room_id: str, event_type: str
     ) -> Awaitable[Tuple[int, JsonDict]]:
@@ -153,6 +154,7 @@ class RoomStateEventRestServlet(TransactionRestServlet):
     ) -> Awaitable[Tuple[int, JsonDict]]:
         return self.on_PUT(request, room_id, event_type, "")
 
+    @cancellable
     async def on_GET(
         self, request: SynapseRequest, room_id: str, event_type: str, state_key: str
     ) -> Tuple[int, JsonDict]:
@@ -481,6 +483,7 @@ class RoomMemberListRestServlet(RestServlet):
         self.auth = hs.get_auth()
         self.store = hs.get_datastores().main
 
+    @cancellable
     async def on_GET(
         self, request: SynapseRequest, room_id: str
     ) -> Tuple[int, JsonDict]:
@@ -602,6 +605,7 @@ class RoomStateRestServlet(RestServlet):
         self.message_handler = hs.get_message_handler()
         self.auth = hs.get_auth()
 
+    @cancellable
     async def on_GET(
         self, request: SynapseRequest, room_id: str
     ) -> Tuple[int, List[JsonDict]]: