You could try Blackberry wood campsite - www.blackberrywood.com - been meaning to go for a while. Looks reasonable, nice setting and allows open fires
Saw this thread when researching for a blog on wild camping regs etc - which this bushcraftuk is a great source for.
I've got two woodland campsites in Sussex - one of which, Beech Estate located in a 600 acre wood we get lots of bivy, tarp and hammock campers at.
Blackberry wood is nice site set on whaty I think is about two acres. Open fires etc.
Bit self serving but I think my Eco Camp Uk site at Beech Estate is as close as it gets to wild camping in England - we are allowed to camp in 20 acres of the 600 acre wood and as long as hammockers etc are sensible we let them 'hang out' in the trees away from the crowds.