From Hounslow your nearest airfields are Heathrow (
AFAIK there's no school there!) Denham, White Waltham, Fairoaks and Booker (Wycombe)
When you've bought your cheap car I suggest you drive to each and visit the various flying schools. (Be aware that at Denham there are two schools in different parts of the airfield and they're very different).
See what kind of reception you get at each, ask your questions and then decide.
Come back and let us know how you get on.