Katy, look at "How to Join a Theme Camp" at the top of the 2011 Theme Camps forum, then look down the list for a camp whose mission speaks to you, so that even if they want 4 hours of work per day and X number of dollars, it'll be worth your effort and expense for the perks of a camp. Then write an email saying why you're right for them--almost like writing a cover letter for a job, but not so stiff or formal. They want to have a good Burn as much as you, so they're selective as you would be if you were inviting people to camp with you.
(Rarely do theme camps recruit. You usually have to go to them.)
You might also click on Regionals at the main Burning Man site and join your local mailing lists. There are London burners, and you should network.
Finally, realize that you don't need a camp to survive. If you can pound rebar, consider buying supplies in Reno or SF and being radically self-reliant, which is one of the Burn's 10 Principles. You can visit theme camps all day if you want, with your time totally as your own.