Along with the South London Theatre, even nearer are a couple of great pub theatres - upstairs at the Hob (opposite Forest Hill station), and the Brockley Jack in Brockley Rise.
The play that I saw recently - 'To W.H' - was brilliant, and I think that has a tie-in with the South London Theatre. From July 24 to Aug 19 'Stay With Me' by Stuart Draper is on, which is billed as being by Melmoth in assoc with the SLT... as a venue the Hob was great, but a bit hot in May - it could be very steamy by August! The bar area of the Hob is good too - very relaxed, lots of sofas, nice staff, etc.