We have stayed at Cavalier Fields three times now. It used to be listed on the Silverstone web site camping page, but got knocked off last year.
It is a couple of miles from the circuit (Luffield corner), but we take bikes and cycle in. We also like the Fox & Hounds pub in Whittlebury, which is on the way to the circuit.
Cavalier Fields is quiet, well drained, friendly and not as expensive as closer camp sites, but still has a good atmosphere. Don’t go there if you want to be camped on top of your neighbour and party all night (please!)