You know that joke about two people being chased by a bear, and one only having to run faster than the other.
Well it's the same thing with UK v other countries' banks, especially US banks.
As long as we aren't more exposed and out on a limb than most of them we'll be fine (relatively speaking).
Actually, being a "safe haven" relative to places like the US might be almost as bad, if that caused foreign currency to flood in and raise sterling.
So I guess the trick is to try and position oneself as no more and no less precarious bank-wise than any other (sane) country.