As I presume everyone is talking about light singles it is interesting that noone has mentioned 'Rule 5'. By my reckoning you would need to be able to glide about 3-4nm to abide, which puts any suggested route for your average spam can at about 3000' minimum.
Personally I am not convinced of a need to endanger commercial traffic because someone thinks it would be fun to fly over LHR. And before anyone criticises me on that one, it certainly wouldn't make it safer, and more planes in the area must by default increase the risk of an incident/accident.
Besides, there is always plenty of VFR traffic in the various control zones in the south east. On a good VFR day I normally hear a couple of infringements a day whilst out flying.
It would also be a great opportunity for terrorists to access the airport.....