Let’s get one thing straight. The blame for last week’s Brexit vote rests with David Cameron – both for calling a referendum for which there was no widespread public demand, purely to manage internal strife within the Conservative party, and for the way he timed and framed that vote. Blame belongs too with the leave campaign, who won their mandate on a false prospectus – dishonestly promising that a British departure from the EU would bring a £350m weekly windfall to the NHS and would halt EU immigration. Bogus promises which won over many millions of voters but which were cheerfully discarded within hours of victory. History will not forgive them.

Let’s get another thing straight. What matters most in the coming months and years is the reshaping of Britain’s relationship with the European Union. For that reason, it matters who will be doing the reshaping – which is why the contest for the Tory leadership is significant. Compared to both of those, the current psychodrama of the opposition Labour party is a mere sideshow.

Nevertheless it is unfolding before our eyes. Given that there could be a general election this autumn or, perhaps more likely next spring, the state of the opposition could have a real bearing on how Brexit plays out.

Corbyn, McDonnell and their inner circle betrayed the hopes of the generation that believed in them most

So we can’t ignore it. As I write, Labour’s MPs are in revolt against their leader, Jeremy Corbyn. He insists he is staying put, even unveiling a new shadow cabinet team on Monday morning to replace the one he lost through the weekend’s mass resignations. Deputy leader Tom Watson has told him he has lost the confidence of his MPs. The next step is likely to be a vote of no confidence which, if it passes, would trigger a leadership contest with the current incumbent as a candidate.

At which point two key facts will become crucial. First, Corbyn’s base – the source of the enthusiasm and momentum which carried him to his famous victory last year – was the young. Second, the young voted overwhelmingly to remain in the European Union. Indeed, if 75% of all 18-24 year olds who voted, voted to remain we can reasonably presume that figure was even higher among the left-leaning idealists who flocked to Corbyn a year ago.

Which means a key question in the coming leadership contest will be: to what extent do those young Labour party members and registered supporters blame Corbyn for remain’s failure last week?

Before the weekend, I would have suggested that the fair answer would be: a bit. He had never been more than a lukewarm advocate for staying in the EU and it showed. His performances were flat and he couldn’t hide his own lack of enthusiasm. He confessed to his own tepidity when he rated his own commitment to the cause as no more than a “seven or a seven and half” out of 10. And nor did he help those Labour campaigners, encountering deep misgivings about immigration on the doorstep in traditional Labour areas, when he chose a set-piece interview with Andrew Marr on the Sunday before polling day to say that he did not see either the possibility or the need for an upper limit on migration – and all but agreeing with Marr that if you had concerns about immigration your best bet was to vote leave.

So none of that was exactly helpful. But Labour members couldn’t claim to be shocked: Corbyn had hardly sold himself in 2015 as a passionate campaigner for the EU.

Yet this weekend provided evidence of something much more serious. The BBC’s Laura Kuenssberg and others have seen the documents which prove that Corbyn and his top team were guilty of much worse than a lack of enthusiasm. They engaged in “deliberate sabotage” of the remain campaign. They pulled out of critical media appearances at the last minute, or else passed up media opportunities to make the case against Brexit; they removed pro-EU lines from speeches; they repeatedly diluted the official Labour position of support for in.

My own reporting, speaking to those involved with the in campaign, confirms this account, as does Phil Wilson MP, parliamentary chair of Labour In For Britain. At those moments of the campaign when Labour was to be given the floor, the party had either prepared nothing or used its platform to attack the Tories fronting the remain campaign, rubbishing George Osborne’s warnings of the economic consequences of Brexit for example. There were plans for a dramatic intervention by all Labour’s leaders – past and present – to stand together and call for remain, designed to ram home to Labour supporters where their party stood. But that was scuppered by Corbyn’s refusal to be associated, even indirectly, with Tony Blair. One idea would have seen Blair in Belfast, Gordon Brown in Glasgow, Neil Kinnock in Cardiff and Jeremy Corbyn in England – but Team Corbyn said no to that and every other version of the plan.

Accompanying Labour canvassers in Yorkshire 10 days before the vote, I saw the effect for myself: Labour voters were still unclear whether their party was for remain or leave, and they were certainly not getting the unmistakable message that a vote to leave would be catastrophic for them in particular.

The young idealists who rallied to Corbyn in 2015 need to bear this in mind if and when they come to vote on his leadership. Many in that generation are in a state of mourning following the Brexit vote. They know that their own opportunities have been sharply reduced, that they may well be deprived of the freedom to work and live and seek out new possibilities in Europe. They should know that the outcome they dearly hoped for was undermined by Corbyn, John McDonnell and their most senior lieutenants.

Perhaps that was because those men had never moved on from their 1975 opposition to the European project, still deeming it a capitalist club. Perhaps they were never that bothered by the prospect of Brexit. Perhaps they thought economic chaos and Tory divisions might create a political opening for Labour. Whatever the motive, the facts are plain: Corbyn, McDonnell and their inner circle betrayed the hopes of the generation that believed in them most. The young helped put Corbyn and friends in. Soon it will fall to the young to push him out.