Not necessarily. There are people like myself, who look at our history, and see that involvement with Europe has always ended up costing us. In 1066 we lost our last English King and we haven't had one since. Centuries of long and costly wars with France - mostly promoted by the ambition of our (French) Kings, ended in civil war, followed by religious conflict stoked by Rome.
The current lot of (German) monarchs had us at war with France again up until 1914, when we switched sides and started to fight the Germans. We did that, on behalf of France, twice in a century at great cost and with barely a nod of thanks.
A trade agreement with Europe (the Common Market) was fine and we'd happily continue with that. But political union with a continent that is still a battleground (however polite) between France and Germany was just too much to swallow. We'll take our chances with prosperity if it keeps us out of another war.
BTW, a lot of us are getting fed up with the US throwing its weight about as well, so tread carefully or we'll throw you out, too!