I think its a little harsh to say that its non-existant.
The main sports teams for women are the football, rugby, basketball and to a lesser extend tennis teams.
The ladies football and rugby teams in particular are particularly active in terms 1 and 2 as far as I know.
Sport in general is slightly harder to get into at SOAS i guess. Its not that its not there, its just not it not as important for most SOAS students compared to other unis.
If you want to play squash, table tennis etc. then some of the intercollegate halls have the facilities. Plus there's ULU which has a badminton team, Taekwondo and Karate, which students from University of London can get involved in. If you join the gym at ULU you've got all the facilities there plus a rather nice swimming pool. Its pretty pricey though at £26 pounds a month, but is reasonable if you use it often.