Sorry - just visiting again and saw this thread. There is an additional irony with regard to the non-binding nature of the referendum. It was ruled that there were significant irregularities with the vote leave campaign, namely that they spent more than they should have. If this had been a binding referendum, then it could have potentially have been ordered rerun by the courts. However, the courts cannot do so with an advisory referendum.
I hope I got that right. Here's a related article:
Brexit: Vote Leave broke electoral law, says Electoral Commission - BBC News
Also, you mentioned earlier why there was a problem with rerunning the referendum now to see if people want to leave now we have a clearer idea of the deal we will (or won't) be getting. The argument tends to be that it would be anti-democratic to rerun a referendum before the thing that the first referendum was about was implemented. This would be because if the government didn't like the result they got, they could keep running referenda until they got the result they wanted.
My personal take is that the first referendum was anti-democratic. It was just terrible. No supermajority required. No minimum turn-out required. An assumption that remain would win, so no clear idea of what leave might be (which in played into the hands of leave, who ran two independent campaigns promising different things to different people). David Cameron might end up being responsible for one of the most significant political mistakes in living memory.
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