Try the East Dulwich Writers' Group at http://www.edwg.co.uk, email info@edwg.co.uk. Despite the name, members come from all over SE London.

Meetings are Saturdays nights and mid-week, usually about once a fortnight, but most people go once a month, less or more often depending on what they are working on. Mix of published writers right through to absolute beginners. Meetings are very productive and the members are lovely (yes, I am one). The group has self-published two anthologies and the last one won a national award (more details on the website).

I believe there is also a writers' group based at the bookshop on Kirkdale in Sydenham, but I don't know much about it.