I'm going to add a couple more notes:
The price you pay for the gym will dictate the body types.
I received a Holmes Place membership for Christmas for the Kensington High Street branch. Very pretty, classical music in the changing rooms, pretty Moulton Brown soap/shampoos and a wonderful reflective ceiling above the 25 meter lap pool. Everyone in there had money and the body to go along with it. So if you are a serious body builder, not exactly the place to go as everyone seems to be there to show off. Most of the women, in my opinion, just went for the steam room, spa and tanning beds.
I canceled that quick and now have a lovely membership at half the price per month at a one off gym where all sorts of sizes go close to home. They just want to get fit, not exactly a place for serious weight lifting. Not much space.
Keep in mind that in London there are brances of Gold's Gym and LA Fitness which, although I've not been to either of them, they will likely be similar to their counterparts at home.
I found this place in Hounslow
http://www.championgym.co.uk/links.htm for serious weightlifters. Also, Robb, you can enquire with the British Weightlifters Association (
http://www.bwla.co.uk/).