Most Boxing or Kickboxing establishments don't usually require you to become a member or sign a lengthy contract. More traditional Martial Arts such as Karate, Kung Fu, TaeKwondo (some Kickboxing academies) etc require some sort of membership to a governing body so that you have their insurance and can take gradings.
A quick search on Google will bring up a multitude of various disciplines in central London. Unless you can get a personal recommendation it is always advisable to watch a class to see if you like the format, instructor or other participants.
Some of the best gyms can be very testosterone enhanced and make women feel uncomfortable.
If you are not phased by sweaty man classes it will give you an easier choice otherwise have a look for women-only classes, led by women instructors. You will be surprised how many men run 'women-only' classes.
if you need any help or advice you can contact me at: http://www.toughenup.co.uk/women_boxercise.html