Jeremy Corbyn has offered no encouragement to supporters of a second EU referendum after he called for a vote of no confidence in Theresa May’s government and an immediate general election.

The Labour leader did not refer to a second referendum in his two Brexit speeches on Tuesday evening, and risked antagonising the party’s pro-remain wing, some of whom want him to back another poll by the end of the week.

In his first, longer speech at the end of the full Brexit debate, Corbyn said: “Labour believes that a general election would be the best outcome for the country if this deal is rejected tonight.”

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He argued that despite differences of opinion over Brexit, membership of the European Union was not the most important issue facing the country.

“We need to keep in mind that the vast majority of people in our country don’t think of themselves as remainers or leavers,” he said. “Whether they voted leave or remain two and a half years ago, they are concerned about their future.”

One shadow cabinet member who supports a second referendum said they believed that opposition to a second referendum was hardening among Corbyn’s allies, with senior figures preparing to resist pressure to push for one.

However, Chuka Umunna, a leading campaigner for a second referendum, said Corbyn “would face increasing demands to hold a people’s vote by the end of the week”, assuming May won Wednesday’s confidence vote as expected.

An estimated 72% of party members want a second referendum, according to polling released at the turn of the year by the Economic and Social Research Council, and 89% of those surveyed think it was wrong for the UK to leave the EU.

Michael Chessum, a Corbyn supporter and spokesman for leftwing pro-EU pressure group Another Europe is Possible, said that Labour members would be pleased that Corbyn had tabled an immediate vote of no confidence, arguing that it represented “a great moment of unity for the next 24 hours”.

Another Europe is Possible is already mobilising Labour members in support of a second referendum. Chessum argued that it was important that the leadership moved “sooner rather than later to a people’s vote” and warned it could become a wedge issue if there was a divergence between the perceived position of the leadership and the membership over this issue.

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There have also been divisions among Labour MPs who have been critical of Corbyn, with several senior figures, such as Yvette Cooper and Hilary Benn, preferring to support Tory MP Nick Boles’ bill that would allow parliament to take control of the Brexit process.

Cooper called on May to work with all MPs to find a solution to the impasse. She tweeted: “PM says she now will listen and work cross party but she had 30 months to do that and she repeatedly refused. She cannot just carry on as if nothing has changed.”

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Benn, the chair of the Brexit select committee, said: “The prime minister’s Brexit agreement has been defeated by a majority of 230. Astonishing and unprecedented. The big question now is this. Will she listen?”

The party has a limited amount of time to consider its position because May has to table a fresh Brexit motion on Monday, with a series of amendments submitted by MPs to come in the days after.

The People’s Vote campaign has been considering whether to submit an amendment calling for a second referendum at that point. It would probably be put down in the name of the Conservative backbencher Sarah Wollaston.

However, the Labour leadership’s hostility to the idea is so strong that the campaign has been considering a further delay. Insiders have said they wanted the second referendum option to be “the last one standing” after all other alternatives have been exhausted.

Corbyn’s spokesman said after the vote that “a motion of no confidence can happen more than once”, suggesting the party could try for some time to force a general election.

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The shadow Brexit secretary, Keir Starmer, was expected to listen closely to views within the parliamentary party in the coming days in recognition of the wide range of opinions.

A drop-in session held on Monday with 30 to 40 Labour MPs saw “every shade of opinion expressed”, according to one of those present.

The party’s Brexit policy, signed off at its annual conference in September, said all options, including a second referendum, would be considered if Labour could not secure a general election. But the party’s spokesman said Labour “respects the result of the referendum in 2016, which is why we supported the triggering of article 50”.

Labour insiders said one other option under consideration was an alternative Brexit deal, in which the UK remained inside the customs union with a say on future trade deals and enhanced workers rights and protections, although few believe this is realistic.