For a brief moment, it looked like there might be an unlikely agreement between Theresa May and Jeremy Corbyn to resolve the Brexit crisis by holding a general election. The Labour leader understandably wants one. The surprise was that, according to two Sunday newspapers, Downing Street advisers “war-gamed” a snap election in November as the only way to save Brexit – and, revealingly, Ms May’s premiership – after her humiliating rebuff at last week’s EU summit in Salzburg.

Salzburg summit: Emmanuel Macron urges EU leaders to stand firm against Theresa May

It is true that Conservative whips threaten an election, and raise the prospect of a Corbyn government, as they put pressure on backbenchers to support Ms May’s flawed Chequers blueprint. But such threats do not mean that the prime minister is planning an election.

Indeed, her aides have dismissed the reports as “utter hogwash”. After her woeful performance in last year’s campaign, she would be foolish to risk one. A “Brexit election” would be called only if the Commons voted for one; it is difficult to see Tory and Democratic Unionist Party MPs handing Mr Corbyn a golden opportunity to enter Downing Street.

If parliament rejects both a May deal and a no-deal exit, as is very possible, there is a case for an election. It could be argued that the people resolved the in/out EU question in the 2016 referendum; because the government and parliament had failed to find a way to implement it, the public should elect new ones and issue more detailed instructions.

The problem is that an election might resolve nothing. With the Tories and Labour broadly neck and neck in the opinion polls, another hung parliament would be likely, potentially giving smaller parties such as the DUP undue leverage. Above all, the incoming government might lack the clear mandate that was the purpose of the exercise. Ms May failed to win one for the hard Brexit she proposed at last year’s election. Another one might be no different. If the Tories were still the largest party without a majority after Ms May fought an election on something like her Chequers plan, it could hardly be viewed as a ringing endorsement.

If Labour stuck to its “constructive ambiguity” approach to scoop up the Remain vote while reassuring its Leave-supporting voters, it might lack a clear mandate too. Even amid a national crisis over Brexit, an election would also be fought on other issues – austerity, the NHS, social care, housing, education and whether Labour is fit for government. An election might not provide an answer to the Brexit puzzle.

There is a better route out of the cul-de-sac. Since The Independent called in July for the people to have the Final Say, support for a referendum has grown. The Salzburg summit has increased the chances of no agreement being reached with the EU. MPs would then likely block a damaging cliff-edge departure next March. A growing number of Tory and Labour MPs are coming round to the idea that such an impasse would best be resolved by a referendum.

Intense pressure from Labour’s grassroots members, some trade unions and Labour MPs has forced Mr Corbyn to move a significant step closer towards endorsing a referendum. He has promised to respect the decision the Labour conference in Liverpool makes on Tuesday. We welcome his shift.

However, having twice won the leadership on a promise to give members real influence, Mr Corbyn could hardly say otherwise. He would still much prefer an election, so his allies may try to dilute the demand for a clear commitment to a referendum by 125 constituency parties.

An election would unite Labour, while a referendum would expose divisions between the leadership, which wants to press on with Brexit to honour the 2016 verdict, and those determined to stop it. Len McCluskey, the Unite leader and Corbyn ally, foreshadowed Labour’s difficulties over a referendum by arguing that continued EU membership should not be on the ballot paper. We disagree.

Given the new information about what Brexit really means that has come to light since 2016, we believe that people should be given the right to change their minds. There is evidence that Labour supporters who backed Leave two years ago are doing just that.