I was surprised that very few clubs came up in an internet search I did a while ago for clubs in London. I seem to remember there being one at UCL or was it Westminster Uni... The only other one that caught my eye was one run in a pub but they mostly played blitz.
In the end I found one in West London, it didn't appear in the general 'chess club' search but Ealing has one. If you check out their website at http://www.ealingchessclub.co.uk/ you will see they play in a league with various other clubs in the area.
Of course after all that searching I still haven't had the time to actually go there!
I used to belong to Hackney Chess Club years ago, there were a lot of great people there and quite a few of them are still there:
http://www.hackneychess.org.uk/
Kings Head are propbably the biggest chess club in London:
http://www.khcc.org.uk/start.shtml
If you are over eighty years old, then Metropolitan Chess Club is for you:
http://www.djabri.org/metchess/default.html
Athenaeum Chess Club meet near Soho, which can be fun after matches!
http://www.xs4all.nl/~mariked/