diff --git a/synapse/replication/tcp/streams/_base.py b/synapse/replication/tcp/streams/_base.py
index 2699e466bc..c14dff6c64 100644
--- a/synapse/replication/tcp/streams/_base.py
+++ b/synapse/replication/tcp/streams/_base.py
@@ -16,7 +16,7 @@
 
 import logging
 from collections import namedtuple
-from typing import Any, Awaitable, Callable, List, Optional, Tuple, Union
+from typing import Any, Awaitable, Callable, List, Optional, Tuple
 
 import attr
 
@@ -29,6 +29,15 @@ logger = logging.getLogger(__name__)
 MAX_EVENTS_BEHIND = 500000
 
 
+# Some type aliases to make things a bit easier.
+
+# A stream position token
+Token = int
+
+# A pair of position in stream and args used to create an instance of `ROW_TYPE`.
+StreamRow = Tuple[Token, tuple]
+
+
 class Stream(object):
     """Base class for the streams.
 
@@ -66,7 +75,7 @@ class Stream(object):
         """
         self.last_token = self.current_token()
 
-    async def get_updates(self) -> Tuple[List[Tuple[int, JsonDict]], int, bool]:
+    async def get_updates(self) -> Tuple[List[Tuple[Token, JsonDict]], Token, bool]:
         """Gets all updates since the last time this function was called (or
         since the stream was constructed if it hadn't been called before).
 
@@ -85,8 +94,8 @@ class Stream(object):
         return updates, current_token, limited
 
     async def get_updates_since(
-        self, from_token: Union[int, str], upto_token: int, limit: int = 100
-    ) -> Tuple[List[Tuple[int, JsonDict]], int, bool]:
+        self, from_token: Token, upto_token: Token, limit: int = 100
+    ) -> Tuple[List[Tuple[Token, JsonDict]], Token, bool]:
         """Like get_updates except allows specifying from when we should
         stream updates
 
@@ -128,8 +137,8 @@ class Stream(object):
 
 
 def db_query_to_update_function(
-    query_function: Callable[[int, int, int], Awaitable[List[tuple]]]
-) -> Callable[[int, int, int], Awaitable[Tuple[List[Tuple[int, tuple]], int, bool]]]:
+    query_function: Callable[[Token, Token, int], Awaitable[List[tuple]]]
+) -> Callable[[Token, Token, int], Awaitable[Tuple[List[StreamRow], Token, bool]]]:
     """Wraps a db query function which returns a list of rows to make it
     suitable for use as an `update_function` for the Stream class
     """
@@ -147,6 +156,28 @@ def db_query_to_update_function(
     return update_function
 
 
+def make_http_update_function(
+    hs, stream_name: str
+) -> Callable[[Token, Token, Token], Awaitable[Tuple[List[StreamRow], Token, 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 +235,7 @@ 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 +257,7 @@ 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)