Keir Starmer is battling to keep alive the prospect that Labour could ever support a second Brexit referendum as the party reacted angrily to Jeremy Corbyn’s offer to back Theresa May if she flexes her red lines.

Corbyn had written to the prime minister on Wednesday night laying down his conditions for supporting her deal without mentioning the possibility of a public vote, sparking the furious response from Labour MPs and anti-Brexit activists on Thursday.

Owen Smith says he might quit Labour over Brexit stance Read more

The party’s leadership scrambled to soothe MPs, with Corbyn’s office messaging them to insist the letter simply “builds on Labour conference policy” and that the party would “retain the option of campaigning for a public vote”.

But tensions continued to run high. Former leadership contender Owen Smith said the idea he could be asked to “row in behind” government policy meant he was now considering resigning from the Labour party. Shadow Treasury minister Clive Lewis insisted: “I won’t vote for Brexit”.

“I’m on the frontbench because I live in hope that the party will get to the bit of our conference policy where it supports a people’s vote,” Lewis told the Guardian.

Starmer, who is regarded by many anti-Brexit MPs as their best hope of pushing Labour’s direction, tweeted on Thursday morning that Corbyn’s letter did not “take the option of a public vote off the table”.

Keir Starmer (@Keir_Starmer) This letter sets out in robust terms that the Prime Minister must abandon her Brexit red lines. It does not take the option of a public vote off the table. pic.twitter.com/T0bk7vq8cZ

Matthew Pennycook, a member of Starmer’s shadow Brexit team, added: “Either May accepts them in full and commits to enshrining them in law before exit day or we must move to support a public vote. No other credible options left to prevent a ‘no deal’ Brexit.”

The shadow Brexit secretary helped to draft the letter to May, which was meant as a way of fleshing out Labour’s policy, in consultation with Corbyn’s office. A senior Labour source insisted “it was Jeremy’s letter”.

The letter was welcomed as constructive by Conservative supporters of a softer Brexit, including Oliver Letwin and Nick Boles.

What Corbyn's terms for backing May on Brexit really mean Read more

Corbyn campaigned for remain in the 2016 Brexit referendum, in line with the wishes of the overwhelming majority of party members, but has consistently said that his party will honour the result.

And pressure is coming from both wings of the divided party. Several frontbenchers recently warned that they could resign if Corbyn tried to whip them to support a referendum.

Backers of a people’s vote have targeted much of their fire in the past year on trying to win round the Labour leadership to the idea of supporting a fresh poll. But a carefully crafted party conference motion promising it an “option” which would be “on the table” is as close as they have come.

Some regard Starmer, along with deputy Labour leader Tom Watson, as the most likely referendum champion in Corbyn’s shadow cabinet, but with the 29 March deadline looming, they have become increasingly despondent. “Keir is a bit of a windsock,” complained one backbench MP.

Streatham MP Chuka Umunna, who is widely assumed by colleagues to be close to resigning the Labour whip, tweeted in response to the letter: “This is not opposition, it is the facilitation of a deal which will make this country poorer. A strong, coherent Labour alternative to this shabby, Tory Brexit is absent – it has been since this parliament began. Totally demoralising.”

The sour mood in the parliamentary party was exacerbated by news that Liverpool Wavertree MP Luciana Berger, who has campaigned vociferously for Labour to take antisemitism more seriously, is facing the threat of a vote of no confidence from her local party.

One of two motions tabled against her, according to the Liverpool Echo, says: “Instead of fighting for a Labour government, our MP is continually using the media to criticise the man we all want to be Prime Minister.”

Colleagues in Westminster rallied behind Berger on Thursday night, with former Labour leader Ed Miliband calling her “a brilliant, talented person who I am proud to have as a Labour colleague”, who should be “supported not undermined”.

Ed Miliband (@Ed_Miliband) .@lucianaberger is a brilliant, talented person who I am proud to have as a Labour colleague. She is a powerful advocate on mental health and against anti-semitism. She should be supported not undermined by everyone throughout our party.

The no confidence motions are due to be considered on 17 February. They have no formal force, but disgruntled members could try to rally support for a “trigger ballot”, preventing her from standing as a Labour candidate in the next general election.

Owen Smith was asked by Emma Barnett on BBC 5 Live whether he could “in all good conscience” remain a Labour MP after reading Corbyn’s letter.

“I think that’s a very good question, and I think it’s something that I and lots of other people are considering right now,” said the Pontypridd MP, who was sacked from the frontbench for supporting a second referendum.

He had not yet come to a decision, he said, but “at the moment I may be asked by the Labour party to row in behind a policy decision that they know, and the government knows, is going to make the people I represent poorer, and I think more fundamentally, actually, is at odds with the internationalist, social democratic values that I believe in.

“Because Brexit is ultimately a nativist, nostalgic, rightwing, ideological programme, that was sold on lies, that was deceitfully won, and unfortunately is going, I think, to go through,” he added. “And that must beg questions for those of us who are [coming] from my perspective.”