We love camping, but living in London without a car (or license) we only get to camp at festivals or on land owned by people we know, who can offer a lift.
It'd be great to camp over the August bank holiday. Aside from Crystal Palace (which is only about a 20 minute walk from where we live) is there anywhere nice that can be reached fairly easily from London by train, ideally walkable from a station? Sussex and Kent are particularly easy for us to get to, but would consider anywhere!
Hollands Wood in the New Forest is walkable to from Brockenhurst station (around 20 minutes I think) You would need to book ahead at this time of year. It is a busy site, but set in woodland and you have to watch the raiding ponies with food.