Hello. My boyfriend and I would also be interested. A year ago we asked in the Downside Centre on Druid Street, but they said that anyone wishing to play badminton needs to book the entire hall (costing perhaps £20/hour).
It's worth asking again though, cause things may have changed... And also is it's possible to form a group of 8-10 people, then it would be pretty affordable.
Try the Colombo Sports Cente&Gym in Colombo Street Se1 (off Roupell Street/or Blackfriars Road). There used to be three badminton courts for hire but i believe there have reduced that to one but it is reasonably priced. Also i am looking for someone to play with and if ur interested in a game just drop me a line..
Good luck with the one remaining Colombo Street court. It's almost impossible to book at weekends because, although you can only book a week in advance, it seems that groups and classes can block-book for months in advance. In the past six months I've managed to book it exactly four times, despite my friend and I trying on at least 15 - 20 seperate occasions since last October! Once yo've got it it's great, as you have the hall to yourself.