No matter how you do it, you can generally take a tax credit for taxes paid in the UK. But, depending on what your income is, this is almost a guaranteed way to subject yourself to the AMT - alternative minimum tax. It's not fatal, but it's a royal PITA.

I think Rachel's suggestion is probably the best. Find a good tax advisor in the US who is familiar with issues of foreign nationals, and then find a tax person in the UK. (This stuff is vastly simplified by doing things online!)
Cheers,
Bev