Not correct. Ireland for one is much more exposed.
The UK had a serious recession in 1979-82 (as did the US) and although it was an ordeal, the country pulled through it. Unfortunately, lots of people (both in North America and in Europe) have yet to go through one of these events and it will be a learning experience for them. Most of us will grit our teeth, get on with our jobs and come through it. As we did last time. And the time before that.
Anti-US parties have traditionally never got anywhere in the UK as most people still view the US as our main ally. The lessons of the two World Wars of the 20th Century only reinforce this. The main trading links are in Europe - for sure - but the deep bond with North America remains. Having said that, I suspect that the influence of the US on business/banking over here will diminish considerably.