I had a couple of days there last week. Nice little campsite with plenty of fire pits, although you have to buy your wood from the site rather than bringing your own or harvesting any fallen wood. There are no real locations for pitching a hammock and tarp though, more of a tent site really. There is a little bit of woodland on the farm but it isn't currently being used for camping, might be worth asking but I expect the answer would be no.
EDIT: on re-reading I don't think I was clear, I was refering to Manor Court Farm. Also having re-looked at
UK Campsite there are a number of site that allow fires in East Sussex. Perhaps one of them will be viable?