Remember that all traffic is under radar control so no "flight paths" are laid down. The actual tracks flown by the inbound aircraft will be entirely at the discretion of the radar controllers until they are final approach and then they flight straight to the airfield.
And "final approach" in the case of Heathrow is defined as 7.5 nautical miles from the runway threshold in daytime, and 10nm at night. Aircraft that aren't on the ILS (i.e. the runway centreline) by that point are classified as "late joins" and are reported as such.
The 7.5nm point is pretty well overhead either Craven Cottage or Putney Leisure Centre, depending on which runway is in use.
In practice, of course, aircraft tend to join the ILS and fly a straight approach much earlier than that, which is why Heathrow inbounds are a common sight over Stockwell, Lambeth, Battersea, etc.