"what's the ceiling on this route"
It's not clear which route we are talking about but
IF flying H10/H4 west London to east London (Kew to Isle of Dogs) the ceiling is stepped from 750ft at Kew to 2000ft at Isle of Dogs, more specifically to the west of Battersea heliport 1000fteto the East of Battersea 1500ft.
The main restrictions are related to aircraft overhead coming into Heathrow and City airports BUT depending on the circumstances, it may be possible for ATC to authorise a different route and/or height.
Kew is on the final for a 27 approach to LHR so obviously as commercial airliners are coming in helis need to be low.