If you have the use of camping equipment, the following may be of use:
http://www.visitlondon.com/where-to-stay/caravan-and-camping#Qhw0JJ7cySMJrmga.97
http://www.ukcampsite.co.uk/sites/results.asp?county=London
https://www.coolcamping.co.uk/campsites/uk/england/near-london