I think the nearest 'proper' running club is Dulwich. Have you tried the Fetch Everyone website? They have an ongoing thread called FART (Fetchies Along the River Thames) who frequently meet up for a trot along the river. I've only got round to meeting them once and ended up running with two seasoned marathoners - i've never moved so fast!
If you're interested in joining a gay and lesbian running club then there's the London Frontrunners. We run from St. Thomas's Hospital on a Monday evening and either run to Tower Bridge and back (about six miles) or Battersea Park and back (about seven miles).