Silverstone and Brands Hatch are close-ish to London but both in different directions. Do a Google for the mentioned sites and see if they have any events taking place. Another track is Goodwood or Castle Coombe.
You have to go watch a round of British rally cross. You have ex group B rally cars competing against modern day WRC Focus etc.
These puppies are packing out around 700bhp and can out accelerate an F1 car to sixty!
Look here for dates http://www.rallycrossuk.com/
I've always gone to watch then at Lydden circuit when I'm back over in the UK and its a cheap entertaining day out. I know at Lydden you can actually walk into the pits and chat with the drivers and team etc.
Well worth a visit.