I'm not sure how it works for British Citizens, but as a Canadian I am also exempt, I have to pay the required 30% to the I.R.S. and fill out the "1042-S form".
Once I return to Canada, I go thru the necessary steps to get my money back. It takes awhile, but I've never had any problems.
This site might help you out.
http://www.casinotaxrebate.com/
Good Luck