Accusations of cronyism at the top of the Labour party and a “repeated unwillingness to stand up to the stain of antisemitism” must be confronted if it is to learn from its “catastrophic” election loss, a group of defeated MPs and candidates have warned.

The group says that Labour needs to go “way beyond a simple review” of its election performance if it is to understand why it fell to such a heavy defeat, which left it with its lowest number of seats since 1935. In a letter to the Observer, they say the issue of antisemitism was “constantly relayed back to us on the doorstep”.

The intervention will be seen as an attempt by figures on the centre and right of the party not to allow Labour’s poor performance to be underplayed. It comes amid concerns about a party review of its performance that includes the former Labour leader Ed Miliband. Some in the party fear the review, led by the independent Labour Together group, will struggle to give a frank assessment of what went wrong.

Among the signatories to the letter are Mary Creagh, who lost her Wakefield seat, Emma Reynolds, who lost her Wolverhampton North East seat, Anna Turley, who was unseated in Redcar, and Phil Wilson, who lost his Sedgefield seat.

“The scale of this defeat means we have to look unflinchingly at what went wrong, way beyond a simple review, welcome as that might be,” they write. “We need to be honest about why our outgoing leadership’s reflexive anti-western world view was so unpopular, and address the reasons for that unpopularity. We were rejected on doorsteps not just because of our woolly, changing position on Brexit, or in Scotland, because of our weak commitment to the union, but because the very people we were supposed to be fighting for did not think the policies in our manifesto related to their lives.”

Anna Turley, who lost her Redcar seat, was among the signatories. Photograph: Kirsty O’Connor/PA

They add: “The focus on nationalisation and uncontrolled spending commitments meant people simply didn’t believe us. Sadly, this was particularly true with those most affected by the poverty and injustice that 10 years of Tory government has created.

“Lastly, the cronyism at the top of our party and repeated unwillingness to stand up to the stain of antisemitism was constantly relayed back to us on the doorstep, shaming the traditional values of our once great anti-racist party.

“It is our duty to speak up now, so that our party leadership candidates keep these people at the heart of their campaigns to lead our party. The challenge for the eventual winner is immense. We need to win 150 seats in every corner of the country, gaining votes from a coalition of communities. Labour needs to be in government – and for that, fundamental change at the top of our party is required. Only this will help us recover from the catastrophic loss.”

The letter comes with the race to replace Jeremy Corbyn still unclear, with only the shadow foreign secretary Emily Thornberry and the frontbencher Clive Lewis declaring their intention to run. The date of the election has not yet been set.

Shadow business secretary Rebecca Long Bailey, who had been widely seen as the favoured candidate of the party’s powerful left, is still regarded as a likely candidate, but has not yet set out her position since Labour’s election loss. Party chairman and Corbyn ally Ian Lavery is also keeping his options open, suggesting that the party’s left has not yet settled on a single candidate. Other likely candidates include Brexit secretary Keir Starmer, and backbenchers Lisa Nandy and Jess Phillips.

New rules governing the Labour leadership contest may yet make it hard for some of the potential candidates to win a place on the ballot paper. Each candidate now requires the support of 10% of MPs and MEPs, as well as backing of 5% of local parties or 5% of affiliated members, such as trade unions.