I tried a number of clubs but ended up at White Whaltham just west of Heathrow. It isn't the cheapest but it really is excellent in my opinion.
I had tried one or two other places first but really struggled with instructor and aircraft availability.... WW were brilliant in this respect, could fly most days even at relatively short notice.
By car it takes about 30-45 minutes to get to from central london (assuming Chelsea aren't playing at home!) although I know others who take the train so public transport links are also okay.
The other benefit of WW is that it really is a club... so there is a social life, good food, a good bar, loads of interesting aircraft and very friendly people.... not many other clubs combine all these aspects. Its a nice place to spend time on the ground as well as in the air. I haven't found anywhere else near London quite like it in terms of all round package for a PPL.
Also dropped into Stapleford recently and they looked like a good outfit although not the same sort of atmosphere as WW. Also very easy to reach on the train from the city.
Only thing about WW is it really is just private flying, they don't have the commercial ATPL side that somewhere like Stapleford has.
PM me if you want more details,
GSB