There is a myth doing the rounds in all the commentary on the post-Brexit fallout, one that is slowly congealing into something resembling a ‘fact’. This myth is that Labour voters, turning their backs on the party in droves, delivered a Leave win.

Obviously, many voters in hitherto safe Labour seats did vote to leave the EU, and therefore contributed to the result – but the way people are talking these days it would appear to be only Labour that failed to persuade their voters to follow it. But remember that every single mainstream political party bar UKIP advocated remain, and therefore every single one of them failed to a greater or lesser extent – even the SNP, as we shall see.

In fact, as analysis of the referendum vote by YouGov has shown, 65% of Labour voters from the last election voted to remain. This means that more Labour voters voted to remain than those of any party in the UK.

Only 39% of Tory voters at the last election followed David Cameron and voted to remain in the EU and 61% didn’t. Since the Tories amassed 11,334,576 votes in 2015, this means only 4,420,485 Tories voted to remain.

The Liberal Democrats, who are making out that they are the only 100% committed remain party, suffered a similar problem to Labour – 68% of their 2015 voters voted to remain and, given that their vote share shrank dramatically in 2015, this must mean that they couldn’t deliver 32% of their most committed voters! So, only 1,642,786 of their 2,415,862 voted to remain

As we all know, all 38 of the Scottish referendum constituencies voted to remain in the EU. But the 68-32 margin nationwide translated into only 1,661,191 votes for remain. As for percentages of SNP voters in 2015 that voted to remain, the SNP does only slightly better than Labour and the Lib Dems – 71%, meaning that the SNP ‘delivered’ (I am using this lingo deliberately because that is what is being said about the Labour Party) only 1,032,650 votes for Remain (incidentally, only 14,000 votes more than the number of Scots who voted to leave the EU).

By contrast, the Labour Party ‘delivered’ 6,075,748 votes for remain – by far the largest share of the remain vote.

This is why allies of Corbyn are saying that criticism of his leadership is unfair, that his leadership of the party during the referendum was a success not a failure.

Clearly, Labour is by far the most pro-remain political party in the UK – and this is precisely why Corbyn is in trouble. You don’t need to know that Alan Johnson allegedly accused him of not even turning up for the weekly strategy meetings to recognise that Corbyn’s heart wasn’t really in it when campaigning during the referendum. Despite protestations to the contrary that he did his best, when he did campaign (which to those outside the political bubble appeared to be hardly ever) his speeches on the EU were equivocal, ambivalent and deeply qualified. Some even suggest that he never wanted the UK to remain in the UK anyway.

This ambivalence accurately reflects the ‘hard left’ of the parliamentary party and of the membership – some of whom are openly hostile to the EU and backed Brexit. But it clearly doesn’t represent the 6 million Labour voters who voted for remain.

And so, unlike the Tories, it is not possible for Labour to respond to the referendum result by adopting a pro-Brexit position and leader in order to scoop back the voters they lost to the Leave campaign – and it is unclear to me why Labour should be more concerned about the voters they lost to Leave than the Lib Dems (who lost 32%) and the SNP (who lost 29%).

The argument for sticking with Corbyn goes like this: if they lost so many votes to Leave in their ‘heartlands’ because these voters feel ‘left behind’ by neoliberalism, then how can a more centrist, less left-wing and more committed pro-remain leader ever hope to recover them? This would leave the field open for UKIP to sweep up in those constituencies like Sunderland where it came second in 2015 thereby decimating Labour in its heartlands. Only a left-wing Corbynite Labour party has any chance of averting this.

Perhaps. But there are two clear opposing arguments to this. First, it is not certain that these votes could ever be recaptured; what is certain, however, is that with Corbyn in charge, Labour will never appeal to those voters who voted Tory in 2015 – the so-called ‘centre-ground’ floating voters – that Labour needs to win a general election.

On the other hand, an alternative argument is that people won’t vote in a general election the way they vote in a referendum anyway. This would imply that the referendum issue is the only important issue at work in people’s voting intentions. But this is clearly not the case – the referendum distilled all the complex factors that go into voting intention into a simple binary choice that wouldn’t obtain in a general election.

Moreover, the referendum offered a clear and direct target for some voters towards which to direct their concerns about immigration. Immigration would be an important issue at a general election, but not so unambiguously the most important one – as it clearly was in the referendum.

We can’t automatically assume, therefore, that a more centrist Labour party won’t be able to persuade these voters to back them, at the same time as appealing to those who might vote Labour but didn’t in 2010 and 2015. This appeal will, however, need to be based on actual concrete policies and not the wishy-washy policy ‘positions’ that Corbyn’s leadership has barely begun to flesh out (and, given his allergy to compromise, that he will probably never be able to flesh out). And it will need to be based on something else: people need to see a credible party working towards power and be able to imagine the leader of that party as Prime Minister. That will never happen with Corbyn.

There is a third argument. People didn’t vote Leave because of right or left-wing socio-economic programmes; they didn’t vote for or against economic neo-liberalism. The Leave appeal was entirely emotive and based on striking several chords that resonated with people from working-class and middle-class backgrounds who have not quite gotten used to Britain’s post-imperial decline from top-dog to also ran.

The effects of neoliberalism contributed to this, certainly, both in an objective and subjective sense but the ‘left behind’ voters have responded not to the economic arguments of the internationalist left but the hymns of nostalgia peddled by the nationalist right. Symbolically, the EU represents this decline from imperial autonomy and ‘absolute’ sovereignty (another myth) better than anything else. Just being in it is a stark acknowledgment of that fact.

This nationalism is the only thing that working class leavers in the post-industrial wastelands of 21st century Britain, and the well-to-do leavers in the leafy Tory shires have in common. UKIP will try and play these chords for all they are worth, and it would make no sense for Labour to try and out-UKIP UKIP in this particular Dutch auction. They need to offer something else that tries to make a ‘new deal’ in the post-Brexit landscape that joins the concerns of the centrist middle-class vote and those of the working class communities that have seen nothing happen for them for decades.

This is why it must move beyond the party bubble that Corbyn and his allies focus on. ‘Labour’ is not simply its 500,000 members; it represents more than 9 million voters who, at the last election, cast their vote in support of their Labour MPs. If it is to win power, it needs to represent more.

This is why it disingenuous to claim that the MPs who voted against Corbyn in the no-confidence vote have no constitutional ‘legitimacy’. In fact, given that the UK is a representative parliamentary democracy, these MPs legitimately – and constitutionally – represent the Labour electorate in a way that the party membership on its own does not.

Labour policymakers will need to work out what the ‘new deal’ could be and to do so they must consider four things: first, as John Harris’ eloquent piece in the Guardian today argues, the predicament facing the party is dire; second, Labour needs to win a general election and not simply do ‘not as badly as we thought’, which means constructing a coalition between core and floating voters as New Labour did; third, that it can’t win by returning to New Labour, but neither can it do so by following the Corbyn programme (whatever that is); fourth, that although Harris’ analysis is correct, things may not be quite as hopeless as he suggests: the referendum result does not show that Labour’s voters are leaving the party in droves; indeed, it shows that Labour voters are not significantly less loyal than Lib-Dem or SNP voters, and that they may well give the party a hearing if it comes up with the right message and the right messenger.