Well London puts you at the centre of a pretty good rail system. Two possibilities I'd offer that shouldn't be much over an hour: Booker (High Wycombe Railway station then about 10 minutes by taxi) has two clubs (Wycombe Air Centre and British Airways Flying Club) with the usual collection of Pipers and Cessnas, plus BAFC has a rather lovely Chipmunk.
Popham airfield (Micheldever station then 45 minutes walk, or 5 minutes by taxi) has a range of stuff going on, including a couple of hireable Cessnas, a microlight (closer to LSA than the US ultralight category) school and a small company doing aerobatic training in a Pitts.
Both, needless to say, are in the middle of some great aerial sightseeing.
No doubt somebody can add some other options.
G