If you are in the C&CC there is Chertsey. Not exactly central, but with a good train service into Central London.
I tried it, but found that returning on the earliest "off peak" return left me stranded at the railway station after the public service buses past the campsite had stopped running for the day. Which left me hiring a taxi for the "last mile Home". It is also fairly handy for Brooklands, and Hampton Court, both of which are well worth a visit.
Keeping people waiting is stealing a part of their lives.