Duxford have Tiger Moths available for training and pleasure flights and they would be able to discuss anything specific you'd like to do - sightseeing, aerobatics, formation etc. Or if you feel really brave you could go on a tour of London in their Dragon Rapide.
The Tiger Moth is a lovely nostagia trip, but Stampe and Jungman are rather more exciting for throwing around if you are the sort of flyer with a stronger constitution. They're just less available for hire unless you know the owner, Some places will give you a go in a Pitts Special for a specially dizzying experience, but reading between the lines I doubt that's what you're after.
Flight Experiences at Shuttleworth