My local Concorde I suppose, although the Concorde at Heathrow G-BOAB is actually closer (more of the scandal of Alpha Bravo later!).
Delta Golf is perhaps the most accessible Concorde for people living in London and I think the one of the best presented. For £5 on top of the Brooklands Museum admission you can take the ‘Concorde Experience” which includes a guided tour of the Aircraft and a great AV presentation onboard in the front cabin… It’s as close as anyone is going to get to flying in Concorde today anyway.
Delta Golf had a brief, if interesting life, the British development airframe which achieved the type certification and unlike modern development aircraft never entered airline service. Flying for the first time in 1974 and retiring from flight in 1981 after only 1282 hours, it then became a source of spares for the British Airways fleet stored at Filton. In 2004 Delta Golf was acquired by Brooklands and finally put on display in 2006.
Of course it would be amiss not to mention the urban myth that Delta Golf was used by the Ministry of Defence to test UK Air Defences, simulating Russian Backfire and Blackjack bombers, and demonstrating the vulnerability of the RAF in the process…
Update April 2019
Following on from the example set at Duxford, the volunteers at Brooklands have reinstated the nose drop mechanism, demonstrated here on the 50th Anniversary event in April 2019.