Lisa Nandy has launched a detailed plan for how she would tackle antisemitism in Labour if she becomes party leader, saying it is approaching “make-or-break time” for many Jewish members as to whether they remain in the party.

The Wigan MP, who has been a consistent critic of how the issue has been dealt with under Jeremy Corbyn, said she hoped to rebuild trust and demonstrate that the party would fundamentally change if she takes over.

“My [Jewish] friends in the party have spent the last few years questioning on a daily basis whether they should remain,” Nandy said. “They’ve had to face a lot of hostility from other people about their decision to stay. So this is make-or-break time for a lot of people.

“They need to know that, going forward, starting on 4 April, the party has understood the level of the crisis of trust that we have, and that we’re going to change.”

Nandy’s plan, outlined to the Guardian and the Jewish Chronicle, describes Labour’s recent troubles over antisemitism as “a crisis in the soul of our party” and calls for new measures including a transparent, independent disciplinary process and better education.

Ahead of a leadership hustings this week hosted by the Jewish Labour Movement (JLM) – which declined to formally support the party in December’s election – Nandy said: “A lot of people who have questioned their membership of the Labour party over the last few years will be looking to the Labour leadership candidates to show not just that we have been there, and that we’ve been fighting for them and for the values we’ve always had in this party, but that we’ve spent time thinking about what comes next.”

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Nandy said Labour had shown a “failure or refusal to grapple with this at the highest levels in the party over the last four years”, and said it had been heartbreaking for her and her colleagues to see it labelled antisemitic.

“It’s not true to say that the entire party is antisemitic,” she said. “It’s almost the opposite – I have party members who have fought off the far right here in Wigan for decades. They’ve taken blows in the streets against some of these racists. They spent six weeks standing on doorsteps being called racists in the most difficult election I can remember. They’re tired and they’ve been let down.”

The plan calls for an immediate zero-tolerance policy under a new leader, with the party fully implementing, as a minimum, any recommendations from the Equalities and Human Rights Commission (EHRC), which is formally investigating Labour over allegations of antisemitism. Another instant change would be to lower the threshold for suspending members where there are “credible accusations of antisemitism, Islamophobia or other forms of racism”.

Nandy has also pledged to introduce a new and independent complaints process, saying the existing process “is not trusted to handle the wave of cases the hard-working staff team have faced because of legitimate concerns about political interference” and a factionalised process.

Another promised element would be transparency, with Nandy pledging to share information on disciplinary cases with MPs, local parties, the JLM and the media. The JLM would be brought back to carry out training on antisemitism.

Nandy said the Labour leadership had not learned from mistakes on the issue, and the last four years had left her “very, very angry”. She said the issue was “existential for Labour”.

She said: “One of the most shameful things I’ve ever seen was a group of Jewish women MPs at a parliamentary Labour party meeting begging the leadership to take seriously the need to adopt an internationally adopted definition of antisemitism. The response from the top table was: ‘We know better than you do what constitutes antisemitism.’”

All the other remaining leadership candidates have pledged to take greater action to combat antisemitism, and have backed 10 pledges set out by the Board of Deputies of British Jews.

The frontrunners Keir Starmer and Rebecca Long-Bailey, and Emily Thornberry, all of whom serve in the shadow cabinet under Corbyn – Nandy quit as shadow energy secretary in 2016 – all immediately backed the pledges.

Dawn Butler, who is among the candidates standing to be deputy leader, has not as yet signed up to the pledge. Asked on Sky’s Sophy Ridge on Sunday show why she had not, Butler said she wanted to wait for the EHRC report and then “sit down with the Board of Deputies – we have a discussion with them, we sit down with JLM and we have a discussion with them and we get this right.”