You can get the train into town in now time and grab a taxi into High Weald AONB that begins just on the edge of the settlement. The River Medway, National Trust Standen and Ashdown Forest are all within easy reach and there are plenty of excellent campsites nearby.
Almost exactly halfway between London and England's south coast, the Sussex town of East Grinstead is a popular camping spot for Londoners wanting a quick weekend in the great outdoors. You can get the train into town in now time and grab a taxi into High Weald AONB that begins just on the edge of the settlement.