abaddon
Penultimate Amazing
The problem is that in the UK, the constitution is unwritten, theus parliament may chose whether or not a referendum is binding or not, or even if it is held at all.Setting aside the result of a referendum, by whichever part of government (or even the judiciary), would immediately undermine the legitimacy of those very bodies who owe their right to exist to democracy and the rule of law. If we can bin some bits of democracy and the rule of law, we can bin them all, and if ignoring the result of plebicites is justifiable, then so is ignoring the results of elections. That's just about the definition of a constitutional crisis.
The US, for example, has referenda and they are by default binding because it is written and defined.
UK politicians always resist the notion of binding referenda because it removes power form parliament and hands it right back to the voting public. This is anathema to the political class, who, in the UK have a visceral horror of having actual democracy take hold. Now that it actually has, they have no clue what to do which is why they are all jumping ship.