At Waltham, Avia Special and one other outfit do Tiger Moth flights, which can be as hands on as you like, with aeros optional. Flying a Moth treaches you the true meaning of adverse yaw. There are two Cap 10s for aeros or general jollies. Those who feel timid about aeros ought to try some.
I agree with FFF that the Club's own Supercub is overprticed, but there is a real taildragger instructor to fly it with: Ian Marshall (he also flies the Cap).
At Booker, there is a Chipmunk. At Oxford itself, no taildraggers that I know of, but there is a Slingsby.