The park appears to be owned jointly by P&K Council and the Forestry Commission, I can't find anything on the park website regarding a camping ban, in fact the Forestry Commision gives a little encouragement........
Wild camping
Camping wild in the forest can be fun if you're hardy. Please choose a campsite that’s well away from buildings, roads and our recreation facilities and do your best to leave no trace of your stay. This type of camping is lightweight and done in small numbers, for only two or three nights in a place. Overnight parking of cars and campervans is not permitted.
Go for it!