Mary Poppins is slightly, just slightly, out of date. Is Robin Hood considered a period drama? If so, I can't say that counts. The whole nationality thing tends to get a little blurred in that field.
I'm probably picking nits now.
Probably not... I'd be interested to know how many have tried and failed over there. A figure I suppose is impossible to find out. Also like to know how things go on the flip side. Apart from that muppet from 'Green Street' with the dreadful cockney accent, I can't (right now) think of a single...
American jobs for American workers.
Seriously though, the percentage of British actors in America must be minuscule compared to the amount of American actors in, erm... America.