Mayfair has a good sized steam room in the male changing room with a varied crowd. It's currently closed for maintenance work but should be working from next week.
Clapham has a smaller steam room in the male changing room, but a hot mixed gay / straight Clapham rugby type crowd. It's best avoided around family swim hours as the changing room can get noisy.
I haven't been a for a few years, but Kensington had a steam room in the male changing room last time I visited.
Strand has only mixed spa facilities poolside, but you might see some action in the showers.
Most other clubs I know of (Bank, Moorgate, Wandsworth, Wimbledon) also have only mixed sauna / steam rooms poolside.
I should add some practical points if you've not used Virgin clubs in London before:
Most clubs have an electronic wristband system to secure your locker, so you'll need to ask for one each visit.
In many clubs Virgin now restrict complimentary towels to one per person, so you'll need to bring your own if you want to keep a dry towel for your last shower.