I'd suggest your first port of call would be Kemble, although I don't have any personal experience of flying from there.
I've been with Cotswold Aero Club in Gloucester for over a year now, they're a very friendly club - CFI is a nice bloke and extremely knowledgeable as you would expect, the instructor who has been teaching me is also very good and good fun to be in the air with.
If you're in Swindon then about the same distance as Gloucester but along motorway instead of crappy A road is Bristol Filton - again, no experience of flying from there but I know there are several clubs and Aeros are also based there (they train from Gloucester as well).
Hope that's of some use -- good luck!
Rob