The dump has gone now; where it was is now the west end of the superhangar (new buildings to house aircraft are called hangars, the original ones are still called 'sheds').
Back in the late '70s, I drove round the tracks near the fence of the structures/tunnel site(in the days when there was still a Concorde airframe in structures). I found some tailplanes dumped there which I couldn't identify. Fortunately one had a serial number on it, and a little research revealed they were Valiant tailplanes presumably dumped there after the investigations into Valiant accidents had finished.
You mention the first deck landing Vampire; well of course before that was the Vampire rubber landing deck. The concrete base for this still exists between the new control tower and the runway.