The problem with the UK using nuclear weapons without air supremacy is this:
Nuclear weapons would draw biological and chemical retaliation. The NBC triad are presently considered more or less fungible in theory (although in practice, the C is fudged a lot on). Drop a nuke on someone's city and they'll retaliate if able with B or C if they don't have N. With Japan the US pretty much had air supremacy so they could more or less guarantee delivery without much worry of significant reprisal. That wouldn't apply to the UK even in OTL and certainly not in one where they sat out the war.