Court Sessions is probably your nearest port of call.

Have a look here:
http://sessioneast2.tripod.com/

You've unfortunately just missed the Goose Is Out folk singaround in East Dulwich - not all that far from Streatham, – and their next isn't till July, but they put on a lot of interesting concerts, next of which is tomorrow.

Have a look here:
www.thegooseisout.com