Hi, and welcome.

Sorry for the delay in replying - it's been a busy couple of days here and I've only just seen your post!
I'm not sure how things are at the BHC Club these days (it's nine years since we were last in Delhi), but there was certainly a waiting list for guest membership back then. I've heard they've got rid of the snooker table, which is a pity - it used to be a big attraction in the otherwise often slack evenings in midweek. (Darts night on a Tuesday - I think! - used to be reasonably lively.)
The Hyatt club
was pretty popular, and I'd imagine it still is, though the swimming pool used to get pretty crowded at times.
If you're a freelance writer, you might be able to wangle yourself membership of the Foreign Correspondents' Club (it was over near the Oberoi in our day) - we used to go along on Friday evenings, and it was pretty good fun.
Hope you enjoy Delhi, anyway. We certainly did!