My daughter's gymnastics teacher at school recommended Heathrow, because she thought she was pretty good at gymnastics, and Mayfield wouldn't push her enough. She was on the waiting list for Mayfield and I never heard from them (!) so I decided to take her for a trial at Heathrow. It is the best thing I have done, she LOVES it. She isn't in the squad there (it became clear that what looks amazing at school level is just very good recreational level gymnastics at Heathrow!) but she is in a rec. class above her age group there, on a Friday.
I made the mistake of driving once (never again!) but it's easy by train.
Clapham Junction to Feltham (18 mins direct) and mini cab (5 mins) the other end. (Or there's probably a bus, I haven't looked into it).
Anyway, the journey is not too bad really and it is an amazing club. They have to do a trial first and then the waiting list can be long but it depends on how good your child is and how many kids are waiting etc. We only waited 2 weeks for a place.
Hope that helps.