Monocock,
Its a shame that Thame won't accept you (actually the airfield is next to Haddenham village, a couple of miles from Thame).
You might find that Wycombe is a good alternative. Although its quite a way from Thame there's a fairly frequent train service from Wycombe to the station at Thame/Haddenham (which is right next to the airfield)
There are some private strips in the area, but I don't have any contact details for them
Brooklands