Could britain fight off an invader?

Yes. Being a island is good for defence because any enemy's would have to invade by boat which would get bombarded by the RAF and the navy. also we have forces like the royal marines, SAS, SBS, and the paras plus arguably the best trained army in the world, all these would fight to defend there nation. Fighting to defend something that you care about is different to fighting for something your government cares about, any soldiers fighting would be motivated to defend there friends, family and country.