diff --git a/synapse/replication/tcp/streams/_base.py b/synapse/replication/tcp/streams/_base.py
index 2699e466bc..007b105d4d 100644
--- a/synapse/replication/tcp/streams/_base.py
+++ b/synapse/replication/tcp/streams/_base.py
@@ -147,6 +147,28 @@ def db_query_to_update_function(
     return update_function
 
 
+def make_http_update_function(
+    hs, stream_name: str
+) -> Callable[[int, int, int], Awaitable[Tuple[List[Tuple[int, tuple]], int, bool]]]:
+    """Makes a suitable function for use as an `update_function` that queries
+    the master process for updates.
+    """
+
+    client = ReplicationGetStreamUpdates.make_client(hs)
+
+    async def update_function(
+        from_token: int, upto_token: int, limit: int
+    ) -> Tuple[List[Tuple[int, tuple]], int, bool]:
+        return await client(
+            stream_name=stream_name,
+            from_token=from_token,
+            upto_token=upto_token,
+            limit=limit,
+        )
+
+    return update_function
+
+
 class BackfillStream(Stream):
     """We fetched some old events and either we had never seen that event before
     or it went from being an outlier to not.
@@ -204,7 +226,7 @@ class PresenceStream(Stream):
             self.update_function = db_query_to_update_function(presence_handler.get_all_presence_updates)  # type: ignore
         else:
             # Query master process
-            self.update_function = ReplicationGetStreamUpdates.make_client(hs)  # type: ignore
+            self.update_function = make_http_update_function(hs, self.NAME)  # type: ignore
 
         super(PresenceStream, self).__init__(hs)
 
@@ -226,7 +248,7 @@ class TypingStream(Stream):
             self.update_function = db_query_to_update_function(typing_handler.get_all_typing_updates)  # type: ignore
         else:
             # Query master process
-            self.update_function = ReplicationGetStreamUpdates.make_client(hs)  # type: ignore
+            self.update_function = make_http_update_function(hs, self.NAME)  # type: ignore
 
         super(TypingStream, self).__init__(hs)