This US thread might help. I've read quite a few good threads on this but I've had a search and can't find them. The consensus seems to be volunteer, volunteer volunteer: http://www.zoochat.com/2/becoming-zookeeper-279163/
Some sort of animal care qualification is good, but the main thing is as much experience as possible. As you're in Kingston (my home town!) you've got Chessington and ZSL close by to start getting your hands dirty! I used to work at Chessington and when I was there they were always keen to take on volunteers. Good luck!
I'd agree - volunteering is definitely the thing to do and an animal care qualification can only help.
