NATO's nuclear strategy is an essential part of that balance. To threaten to upset it by refusing to let America base any of her nuclear weapons in Britain would make war more likely, not less likely.
So long as the Soviet Union has nuclear weapons there have to be nuclear weapons somewhere in NATO to deter them from using them.
The US, whether we like it or not, has nuclear weapons. The US is a member of NATO. Possession by the US of nuclear weapons is obviously a deterrent.