Apart from the PFA coaching scheme (which is certainly a good thing, but you can only do in your own aeroplane) most clubs have instructors with suitable aeroplanes happy to undertake interesting training. It is only training for a license that has to be done at a licensed airfield, nothing to stop an instructor taking you off to an unlicensed airfield for some grass-strip training, for example.
Also, if you want to expand your horizons go and do some gliding, a microlight conversion, etc. Shortly you'll be able to hire a microlight as well according to the BMAA.
I'd venture that the problem really is the relatively narrow outlook often put out by schools whose bread and butter is basic PPL training, rather than what is available to the average pilot.
G