Hi Wild,
Not exactly on your doorstep but I have used Broadstone Warren Scoup camp in the Ashdown Forest before. Nice mixed woods but can be hectic during the warmer months with scouts (obviously). I think it should be quiet this time of year though. They do allow fires. Give them a call mate and see if they will allow you on site, a friend organised our visits so I am not entirely sure of the criteria.
Good luck.