Balham Leisure Centre does bouncy castle parties for up to 20 kids. My daughter has had her last 3 birthdays there (the last one last Saturday) and it has worked really well. The kids get to be on the bouncy castle for 30mins, then there are games (e.g. pass the parcel, musical statues) for 30mins. Finally they have their tea. All you have to do is provide the food and the games prizes. It's about £150 for the party.
My daughter and her friends really enjoyed it.
http://ww3.wandsworth.gov.uk/NR/rdonlyr ... thdays.pdf
For larger groups, the Latchmere leisure centre is also good but it's not a private space as such.