1. Britain is hardly going to give up its unique monarchy and constitution. A more like future change would be Britain (or pehaps just England, if Scotland and Northern Ireland want to stay European) joining NAFTA (USMC trade group).
2. Politically, the British are significantly to the left of the Americans, at least on economic and social matters. They also have far fewer civil rights. Also note that if the whole the UK joined the USA, they would get 1 in 6 House seats and radically tip the country to the left. Their Tories are for the most part similar to Democrats, with their Labor party significantly to the left for the USA Democrats.