I actually wrote to the BAA a couple of years ago to request the same thing, and I did in fact receive the courtesy of a written reply. This letter confirmed that the friend that said he shot an approach onto 27L was correct, but that now they didnt allow light aircraft to approach EGLL as "It would be unfair on commercial operators should I block the runway for movements"
At the time, I was quite insulted, having flown numerous approaches into busy airports stateside such as KLAX, and KSNA, and so on, but I did see their point. Nowadays there are so many people fleeing UK over the Xmas break.
I do understand from a controller friend, that ATC are in the position to grant a SVFR approach, but that they are unable to grant a landing clearance, as they are only working on behalf of the operator.
I suggest that if you want to be treated as a responsible pilot, and an equal in the airspace community, that you visit the USA, and shoot approaches to land at somewhere like LAX - or go to South Africa, where they welcome you to shoot approaches into Jan Smuts Capetown!
Its a disappointment....... I know
