Good grief! Let's not be throwing around ASB for things like this.
Wildly improbable? Sure. ASB? Nope.
As
@Alternator says, it will require a dystopia. But perhaps not quite as bad as they posit.
The scenario I think is most plausible runs like this.
1) major European power takes over the continent. (This could be a competent extremist German regime, a Tukhashevsky led USSR, or wwiii immediately following WWII)
2) US is forced to intervene and suffers a million casualties or so.
3) US says 'never again', and declares a total monopoly on any advanced weapons. E.g. Jets, Abombs, etc. Anyone breaking the ban gets visited by InstaSun.
4) the US does allow new states, however, so e.g. Canada becomes 7 or 8 states. Rules for new states list maximimum and minimum population sizes, required literacy rates IN ENGLISH, minimum economic status, etc.
Under those circumstances, Britain will likely eventually cave and join as multiple states. Northern Ireland, Scotland, Wales, and one or two states for England.
Mind, you might get the Netherlands or Norway joining before any part of the UK.