I live in Tooting and I've just joined the Windmilers, they seem like a friendly bunch, and Wimbledon Common / Richmond Park are much nicer to run around than Clapham / W'worth / Tooting.
I was going to say that I know a few of the Chasers who just run with them, then I realised that since joining they all seem to have developed an unhealthy obsession with tris, so if that's not your bag (it certainly isn't mine!) you probably are better off with the Windmilers.
Perhaps I'll see you at a training session some time!
I think you'll find you've got a choice of the Clapham Chasers, who I suppose strictly speaking are based in Battersea, though quite close to Clapham Junction, and they do run on Clapham Common if that's what you're after, or Wimbledon Windmilers, which I'm guessing is further afield for you. If you're in the 3 commons area, either is easily accessible by public transport (or bike).
BMF has its merits, but it's not a running club - the 'running club' sessions are just their usual fitness classes concentrating on legs rather than the whole body.
Anyway, this seems to be a pretty comprehensive list: