Britain was an important staging area for attacks on Germany itself, and yes they were an integral part of the allied force. That's why we wouldn't have let Hitler conquer Britain, before he established roots there like he did in Europe we would have brought the calvary in, from Iceland and Ireland, even if Roosevelt had to lie us into it. It's all hypothetical, but I think contingency plans had been made for such a possibility.
Btw, great screen name, that's a game I can play forever.