I agree with everything you say, Kevin, except for this:

"If it's down to prerogative power, the government (ie the Prime Minister) has the power to ignore the result of the referendum entirely. In the light of increasing evidence of the harm that Brexit promises to cause to this country that would be perfectly correct constitutionally."

Prerogative doesn't come into this as the referendum was advisory. If she decided not to accept the result she would merely be declining the "advice" of 37% of the electorate. There is no constitutional issue there. Prerogative, on the other hand, IS a constitutional issue, fought for in a civil war to stop ignorant kings and queens ruling by diktat and successfully defended for hundreds of years. Hence the court case. If she decided to reject the result (the right thing to do, though politically suicidal), no doubt somebody or other would pursue it in the courts but they would have their case thrown out. As the referendum was advisory, remainers would have just as strong a case as brexiteers for complaining about her decision on the advice given to her by the referendum, as they could argue that only just over one-third of the electorate advised her to leave, all of which would lead to an absurd situation. Advisory means that the government asked for advice. There is nothing in our constitution that says that advice MUST be followed, regardless of what "promises" about it were made in advance of the vote. But there are safeguards in our constitution that protect parliamentary sovereignty. It would be beyond amazing if the Supreme Court overrode the High Court - worse, it would be downright suspicious.