The London campus has expanded to several buildings in the same neighborhood. It operates on the British system and is fully accredited by the relevant British authorities. It is not an American university operating as a branch campus in London. But the American influence makes for a sort of blended British/American vibe.
European universities in general lack the “campus culture” of American universities and students are mostly on their own to develop a social life.
Doing a fourth year in Boston and earning an American degree in addition to a British degree would be appealing to certain employers. As for coops in England for Americans, it would be best to contact Northeastern directly.