Jeff, There is a good C&CC CS at Syresham which is off the A43 west off and close to Siverstone.
Lakeside View, High Cross, Syrenham NN13 5TJ MR 152/620406 01280 850480.
I have stayed there a couple of times en route from the South coast to the North East, it is a small site in the grounds of the owners house with a small lake / pond. I am sure that they would take you as a CC member, they have never asked to see my C&CC card.
Ray