Best club at Biggin Hill is the Surrey & Kent flying club
Google that for more info but i do know is to go London Victoria and take the train to Bromley South (approx 30 minutes ride) and then from out side Bromley South station take the 320 bus to Biggin hill airport (approx 30 minutes)
Oh and bring lots of dosh with you as flying in the UK ain't cheap!
Enjoy your stay
TBE