HA, The London TMA begins at 2500 ft. The LHR control zone is from the surface, so you wouldn't be avoiding it.
You would also need to comply with the "land clear" requirement:
(d) The land clear rule
An aircraft flying over a congested area of a city, town or settlement shall not fly below such height as would permit the aircraft to land clear of the congested area in the event of a power unit failure.