Ohh a thread on which I have a small amount of knowledge!!
There is free camping in a field at the track (first come first served I assume as they do not issue tickets) with very basic toilet/water facilities. You drive in with your car and set up, she didnt say anything about having to park elsewhere.
It is at the track, but not sure if its infield like Silverstone or not.
We are allowed to bring in "a reasonable amount of beer"....

You could always give em a ring and ask for more factual information tho - or perhaps someone else has been there before.
Checked out paddy's link, but they refer to a private campsite not available to the public - so I dont think this will be the same facilities that Donington itself is offering - especially with the mention of "showers"!!
Just checked AGAIN - and it says "We are based in the grounds of the Park Farmhouse Hotel which is located at the competitors entrance to Donington Park Racing Circuit".