If Rockingham and Silverstone are a bit much, try to get over to Brands Hatch to see the locals have at it. There used to be a BTCC round there as well; I attended one in the late '80's. It's easy to get to from central London (it's in Dartford, and there's excellent rail service to and from). It's a beautiful track, with a lot of history (used to host the British GP).
