I wasn't sure whether to reply to your thread as I'm not sure if what we do would interest you if you're looking for a Pure running club. But if it's more the social/getting outside/exercising aspect you're after, then my colleague and I have just started up a bootcamp circuits class at Tanner Street/Bermondsey Street park.
If you're interested, take a look at my website which has some more details www.fitns.co.uk
Sorry if this isn't quite what you were looking for, but thought I'd mention it on the offchance :-)
Not exactly SE1, but there's a ladies group that runs from the Sweaty Betty shop near Monument on Tuesday nights at 6:15. The run is usually around 5k and includes dynamic stretching, drills, etc., so it can be quite a workout.
Once you've turned up once, the organizers will send you an email on Monday nights so that you know what the plan is for Tuesday, and to just confirm that the run is on. This week it's not on as the "coach" is out of town, but I'm sure it will be back on next week!