Jeremy Corbyn is running out of road – he must face up to Labour members’ call for a Final Say referendum

Corbyn has used up one of his excuses for avoiding the new public vote he does not want but which his party does

Tonight’s Commons votes on Brexit have implications for Jeremy Corbyn as well as Theresa May. The Labour leader will now come under further pressure from his MPs and party members to back a Final Say referendum.

Corbyn has used up one of his excuses for avoiding the referendum he does not want but which the Labour conference – the party’s policymaking body – voted for in September. Under the sequencing plan it approved, Labour would seek a general election and, if that failed, would put all other options on the table, including a “public vote”.

His attempt to force an election via a vote of no confidence in the government failed two weeks ago. Another part of the sequence was to get a proper hearing for Labour’s alternative Brexit deal – based on a permanent customs union. That box was ticked tonight, when Corbyn’s amendment outlining his plan was rejected by 327 votes to 296.

So in theory, Labour moves a step closer to supporting a Final Say vote – a necessary ingredient if a Commons majority is going to be forged for one. In practice, Corbyn is unlikely to undergo an overnight conversion. Like May, he is playing for time.

Corbyn has dropped his refusal to join May’s all-party talks following the vote on the Caroline Spelman amendment which MPs used to express their rejection of a no-deal exit. The vote was non-binding, but it allowed Corbyn to put an end to May taunting him for boycotting the discussions; he had refused to attend until she ruled out a cliff-edge departure.

No one should expect a meeting of minds when the two leaders finally sit round the same table. Neither is a consensual figure, both are tribal animals. Corbyn will argue that a customs union could secure a cross-party Commons majority. But May knows that relying on Labour votes could split her party; her strategy is to hold it together.

The Commons debate highlighted the strain the Brexit endgame is putting on Corbyn’s strategy of constructive ambiguity on Brexit, which has largely masked Labour’s divisions. There was always going to come a point when sitting on the fence – and sending different messages to Remain and Leave voters – would become untenable. Now it is happening.

The shadow cabinet agonised over whether to support Yvette Cooper’s amendment calling for a backbench bill to extend Article 50 by nine months to December. Key Corbyn allies such as Jon Trickett warned that backing the Cooper plan would be seen as delaying Brexit and risk alienating millions of voters.

Corbyn, nervous about being accused of blocking Brexit, found a third way: whipping Labour MPs to back Cooper to prevent a cliff-edge exit in March, but shortening the extension she proposed from nine to three months. But 14 pro-Brexit Labour MPs defied him by voting against the Cooper move, ensuring its defeat.

Corbyn had an uncomfortable time in the Commons. His below-par speech was eclipsed by Cooper, who as a former shadow home secretary and May’s opposite number found a chink in her armour, questioning her more effectively than Corbyn. Cooper is a member of the “shadow, shadow cabinet” of Labour centrists who languish on the backbenches under the Corbyn regime.

The Labour leader’s own speech was interrupted by Tory MPs making bogus points of order. He was ridiculed by Tories for refusing to take a question from Labour backbencher Angela Smith, who wanted to ask him when he would honour the Labour conference decision on a referendum.

Corbyn presents Labour as the only party that can unite a divided country, but does not want to be portrayed as either enabling or scuppering Brexit. Close aides believe that backing a referendum would put at risk the coalition Labour needs to build to win a general election. Its target seats include some in the north of England and the Midlands which voted Leave in the 2016 referendum. Endorsing a referendum would demolish Corbyn’s insurance policy with these voters: saying he respected their decision in 2016.

Corbyn was once keen on online ballots of party members to give them more say over policy, one of his pledges when he ran for the leadership in 2015. He is less keen on a members’ vote on Brexit, as he knows what the answer would be: opinion polls show that seven in 10 support a Final Say vote and would back Remain.

Hopes of referendum campaigners were raised briefly when Corbyn mentioned a “public vote” in Labour’s amendment for the debate. Although the pressure on him will now mount, he will likely continue to resist it. One Labour frontbencher who backs a referendum told me: “A few weeks ago I thought he was slowly coming round to it, but now I am not so sure.”

Corbyn rightly attacked May for “the absence of any leadership”. But on Brexit, some Labour figures are aching for him to show more of it himself.