Oh boy! More nuclear weapon contingencies to think about this afternoon.
If things were to ever fragment to the point that the Acts of Union are dissolved and all the major nations of the British Isles emerged as totally independent states, it's a pretty high probability that the English would be the inheritors of the UK's nuclear deterrent. Given the SNP's policy on nuclear weapons in Scotland, the Royal Navy would phase out Clyde and Coulport and move southward.
The most likely outcome would be for England to establish an umbrella policy for the newly independent states of the British Isles, very similar to the measures put in place by the United States with respect to Germany, Japan, and South Korea. However that's by no means a foregone conclusion and, even if it was, putting the defense and diplomatic framework into place could take at least a decade. A lot can happen over that period of time and, depending on local animosities bleeding into the political sphere, there's a potential for some off-the-wall scenarios.
If things devolved to a point that even the 1560 Treaty of Edinburgh was untenable, then there's a very non-zero chance that Scotland might request French support as a strategic nuclear counterbalance in a modern version of the Auld Alliance.
And the nuclear deterrence community thought India vs. Pakistan would be the flashpoint for the next nuclear conflict.