Sorry, can't help you out..... I only know of one Cruelty Free salon (and it's in Australia, even more of a hike than London I'm assuming :P).
What you 'could' do, is ask the salons in your area about the products they use and if none of the products are cruelty free, whether it would be okay for you to bring your own for them to use on your hair. There's a number of salon grade hair products out there now De Lorenzo comes to mind, they're vegan. But John Frieda and Kevin Murphy are also cruelty free from what I've heard, but they might have animal bits in them so it depends on what 'cruelty free' means for you.
Best of luck!