When they unexpectedly seized control of the Labour Party in 2015, Jeremy Corbyn and John McDonnell spoke privately about a “five-year project”.

Given the prospect of a general election after the Conservatives choose Theresa May’s successor this year, there is no immediate need for Corbyn and McDonnell to review their mission. But some of their grassroots allies are starting to contemplate how long Corbyn should stay on if the Tories avoid an election.

Next year, ringed in the calendar by the Labour leader and shadow chancellor as the likely date of the next election, might then mark the beginning of the end of Corbynism.

“People are starting to think about life after Jeremy,” said one Corbyn loyalist. It is a process that will gather pace now that Labour’s national executive committee (NEC) has rejected grassroots calls for the party to support a Final Say referendum on any Brexit deal. Corbyn now risks alienating the very members who ensured his 2015 victory.

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Labour will merely keep open “the option” of a public vote if May refuses to change her deal, to prevent a no-deal exit or if Labour fails to secure an election. Corbyn’s “constructive ambiguity” allows him to be all things to all people. He can reassure Leave voters in the north and midlands that Labour respects the 2016 referendum decision. He can nod and wink to Remainers that a Final Say vote has been put “on the table”, though it is difficult to imagine the circumstances in which Labour would ever eat it.

Corbyn is prepared to risk a hit from Remainers at this month’s European parliament elections in an attempt to enhance his appeal to Leave voters at a general election. But his electoral logic is open to question. Public opinion has not been frozen since 2016. The polls now average 54 per cent for Remain and 46 per cent for Leave. Anxiety about immigration has fallen.

Even in Leave seats, a majority of Labour voters backed Remain. The British Election Study found no marked difference between 2015 Labour voters generally (63 per cent backed Remain a year later) and in the north (57 per cent) or midlands (60 per cent). Rob Ford, a professor of politics at Manchester University, warns that Labour could alienate Remainers by wooing Leavers, who might not be won over because the party supports a customs union.

He points out that Brexit is not the only issue motivating voters. “If it was, then May would have won a lot more Leave-voting Labour seats in June 2017,” he said. Several Labour MPs representing Leave constituencies in the north reject its caricature as “Brexitland”, insisting opinion has shifted and that the regions now support a referendum.

Corbyn cannot assume that Remainers who backed Labour at the 2017 election will stomach his refusal to give a clear-cut pledge of a referendum. On 23 May, these voters will have somewhere else to go: the Liberal Democrats, Change UK, the Greens, SNP and Plaid Cymru. Alastair Campbell, tribally loyal to Labour, told the BBC’s Politics Live programme yesterday he did not know whether he could vote Labour because of its referendum stance. He will not be alone. If a general election were dominated by Brexit, such voters might not come home to Labour.

Corbyn is also storing up problems for himself. Ironically, given his allies’ default position of dismissing all critics as “Blairites”, his office uses the Blair “command and control” playbook to stifle Labour grassroots demands for a referendum.

There was a time when Corbyn, having promised his party’s members greater say over policy, favoured e-ballots of the membership. He would not dare to call one on Brexit: it would show overwhelming support for a Final Say referendum and Remain.

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In a timely new book about Labour, Protest and Power, David Kogan warns: “If Jeremy Corbyn suddenly appears to be an old-style Labour leader by failing to listen to the membership, taking advice from a small coterie of advisers and using the power politics of yesteryear, the danger is that the wide support he gathered in 2015 and 2016 from new, young members of the party will suddenly disappear.”

Indeed, there are growing signs of disillusionment among Corbyn’s natural supporters over Brexit. Its pro-EU wing, which mobilised itself under the slogan “Love Corbyn, hate Brexit,” has spawned a new group of Labour MPs: “Love Socialism, Hate Brexit.” There are other straws in the wind. Many in his Momentum fanclub part company on Europe, including its national director Laura Parker.

After all nine constituency party representatives toed the Corbyn line at yesterday’s NEC meeting, there is now talk that his new friends in Momentum could end their joint left-wing slate at future NEC elections with his old allies in the Campaign for Labour Party Democracy.