Some of Labour’s most influential figures are urgently warning Jeremy Corbyn to change his approach to antisemitism, Brexit and factional infighting, as more senior politicians reveal they have already decided to quit the party.

Figures across the party say that a major exodus of MPs, peers and councillors will be triggered over the next few weeks unless the demands for change are met, with some already poised to go.

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One senior parliamentarian told the Observer: “I have decided that I am going to have to leave. For me, it’s just a question of when.”

With the Labour leadership battling to contain a wider split after the resignation of nine MPs last week:

• London mayor Sadiq Khan is warning that the party’s response to antisemitism has precipitated a “collapse in trust” between Labour and the Jewish community;

• Tom Watson, the party’s deputy leader, and Keir Starmer, the shadow Brexit secretary, are pushing Corbyn’s team to support a deal to secure a second referendum – with one of Britain’s biggest unions also backing the plan;

• One of Labour’s biggest former donors, Sir David Garrard, told the Observer he has already funded the Independent Group (TIG) of 11 MPs who quit last week;

• Senior figures are also calling for any attempts to trigger the reselection of MPs this year to be ruled out to help calm divisions.

A new Opinium poll for the Observer places TIG above the Lib Dems. It gives the Tories an eight-point lead, with the Conservatives on 40%, Labour on 32%, TIG on 6% and the Lib Dems on 5%. Ukip records 7% support. The Labour leadership is attempting to stem the crisis by promising to review its handling of antisemitism complaints after Luciana Berger quit, following vehement abuse. The leadership is also poised to back a plan by Labour backbenchers Peter Kyle and Phil Wilson, which would see Theresa May’s Brexit deal voted through on the condition that it is put to a public vote. Watson and others see it as a way of uniting the party once Labour’s preferred Brexit deal has been blocked.

The pressure on Corbyn to back a second referendum was increasing on Saturday night, as Tim Roache, general secretary of the Labour-affiliated GMB union, backed the Kyle-Wilson plan.

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“The clock is ticking and something needs to break the logjam in Westminster,” Roache said.

“The prime minister refuses to budge, there is no genuine attempt to get consensus, and no deal would be an absolute economic disaster, so this needs to go back to the public.

“The people must be the ones to decide whether Theresa May’s version of Brexit beats the deal we already have with Europe. If the prime minister is confident that her deal does the job, she doesn’t have anything to worry about.”

In an online article for the Observer, Khan said that the last week had been “the most distressing and depressing of my 33 years in the party”, and that urgent action was needed to keep Labour together.

“It is our responsibility to ensure that the Labour party emerges from these uncertain times ready to govern and able to attract those Members of Parliament who have left to return home,” he writes.

I've observed the intimidation and bullying that has become endemic within the party and its supporters for all to see Sir David Garrard

“Over the last few years, it’s clear that Labour has been too slow at addressing the Jewish community’s concerns and at kicking out the minority of Labour members and supporters who think it is acceptable to use antisemitic tropes and abuse – both online and in local Labour meetings. This has led to a collapse in trust between Labour and the Jewish community.”

His intervention comes as Garrard, who had donated about £1.5m to Labour since 2003, told the Observer that he had already started funding TIG. “I have watched, with ever-growing concern, the deterioration, especially over the past year, of the extent and nature of the naked antisemitism which has increased throughout the Labour party and its supporters, since Jeremy Corbyn and his cabal of revolutionaries took control of the Labour party which I had so admired and supported with commitment and enthusiasm.

Facebook Twitter Pinterest Sir David Garrard: the former Labour donor has already started funding the Independent Group. Photograph: PA/Empics

“From the very outset of Mr Corbyn’s leadership I had feared the ultra-Left Marxist/Socialist nature of the Labour party’s new leadership and its supporters, all of which led me to conclude that a socialist republic for our nation was what these politicians intend.

“I have observed the intimidation and the bullying that has become endemic within the party and its supporters for all to see, and it is therefore with a sense of actual relief and optimism that I’ve witnessed the emergence of these brave politicians who put country before party.

“I am hopeful that there may yet be a bright outcome from the sadness and despair of what was once a proud and courageous Labour party. I’ve been asked whether I will financially support the new group. I have already done so.”

The Labour leader and his team strongly deny any suggestion that they tolerate antisemitism.

Angela Rayner, the shadow education secretary, hit back at TIG in an article for the Observer, saying the group is “now the real barrier to change”.

She added: “From what we have seen and heard so far, all that we know is they would continue Tory policies from endless privatisation to sky-high tuition fees.”

Meanwhile, senior party figures are also calling on Corbyn and his leading allies to agree to delaying the process of reselecting MPs until after this year. Three party sources told the Observer that some of the leader’s allies were keen to start the process, which could lead to the deselection of sitting MPs. A Labour spokesperson said it was “categorically untrue” that any list of seats had been drawn up as part of the first wave of the reselection process.