I was just trying to think of useful resources if you fancied doing some more research.
UK Athletics is the governing body for clubs, although the seach facility for clubs is pretty pants. Also have a look at the UK running track directory although the London map doesn't appear to be working for me at the moment.
Here's a good one - a summary of results for previous years' Southern 12-stage road relays. The road relays are run on a regional basis (Southern, Midlands, Northern, leading to the national champs) and are about the highest standard club races in the country. Any of the London based teams coming in the top 20 places will be showing good evidence of strength-in-depth. Kent AC did rather well this year, coming third behind Newham and Essex Beagles and Highgate Harriers. Then you've got clubs like Woodford Green, Tonbridge (bit further out in Kent), Belgrave Harriers, Herne Hill Harriers, Blackheath & Bromley, Shaftesbury Barnet, Hercules Wimbledon, Hillingdon, Victoria Park Harriers, London Heathside.
These are all worthy of consideration depending on where you'll be based. Obviously the correct answer is South East London and Kent AC. 