In response to user - Chralph, I couldn't reply directly to your question for some reason, so I'm posting this again in case you don't read your private messages. Somebody else might find it useful -

There is a badminton court at forest hill school sports centre.

http://www.foresthillschool.co.uk/31/sports-centre

Think it's £9.50 for an hour, bit pricey but local.

Thanks very much for this update, we played there last thUrsday and although it is pricey it's nice courts and was nice and quiet when we went.

Thanks again to everyone for their responses.

Chralph