The arrogance of politicians was at its highest before the referendum when they didn't bother to make a case for remaining, thinking that the public would simply do as they recommended. After all, if 80% of MPs say remain, then there is clearly no point in pressing the case. And yes, they didn't bother to canvas public opinion before the vote, relying on the sheep to deliver their wishes.
The EU liked Labour's idea for the simple reason that it means we would be tied to them indefinitely, having to adopt every ruling they make and accordingly would have left in name only whilst still leaving us to pick up the bill, without a say.
Have a second referendum and Parliament could probably only offer the single option of 'tick here to remain', with them having voted to reject no deal which was the only other viable option. We should not underestimate politicians' contempt for public opinion. People on all sides of the divide(s) have rightly become very cynical of anything MPs say or do.
The question of what happens next and its timing is moot. As it stands we leave on the 29th, but even a negotiated extension to article 50 won't satisfy the remainers because we will still have passed the cut-off date to rescind it. There might have been an EU ruling that we could rescind the decision unilaterally, but that would surely expire on departure day. Irrespective of views on whether it is right or wrong, a second referendum would therefore only be of any use if the legislation had already been repealed. Otherwise, we would have to re-apply to join the EU with the attendant problems of having to join the Euro as a new member, sign up to Schengen, pay even more per month to a system that would give us little in return, not to mention the views of various member countries as to whether they would want us back in. Joining the Eurozone would merely cement our position of weakness given the overwhelmingly strong position into which Germany is locked via the Euro exchange rate. One thing is certain, they wouldn't let us join the Euro at a rate 10% below the status quo. I can see Germany welcoming us back as another net contributor, but French opinion might not be so favourable as they stand to increase their political clout following our departure. Ireland aside, I think most member states would be indifferent to our remaining as they have little to lose if Germany picks up the tab - quite affordable given its trade balance. I also think the EU would be very reluctant to offer us anything in the way of EU infrastructure in case we decided to leave again. All in all, we are still better off leaving than being tied up in a straitjacket at the whims of the other 27.
On the plus side for the EU, I read today that the woman replacing Merkel had suggested they stop relocating the circus to Strasbourg every month and remain in Brussels permanently. Cue French disagreement (for which read hurt pride) - yet hypocritically claim to be pressing for improved environmental pollution targets despite the unnecessary mass movements from monthly relocation. She also suggested that EU officials should be put on the same tax basis as the rest of the population - perish the thought. Maybe the EU's core is having a few internal rumblings. Shame it's too late.