As far as I am aware, you are only allowed to take S/Es through the Heathrow zone, to the west of London. I understood that neither S/E fixed-wing & helis are allowed over the central & eastern parts of the Heathrow zone.
Even taking the western route, you are rarely allowed above 1500' & sometimes not above 1000' so there is not much scope in a S/E to have sufficient height to glide clear, over the build up areas.