Labour leadership candidates are being warned against trying to “out-working-class each other” as the party weighs up who would be best placed to win back seats lost in last month’s bruising general election.

Keir Starmer, Jess Phillips and Rebecca Long-Bailey have all defended aspects of their backstory as the candidates compete to win over Labour members by highlighting their humble origins.

Ian Lavery, the party chair, whose majority in Wansbeck was slashed to 814 in December, said it was the candidates’ policies and life experiences, not their parents’ jobs, that were most important.

“What has been pretty infuriating is that candidates have been trying to out-working-class each other,” he said. “It’s like we used to say in the school yard: ‘My dad is bigger than your dad.’ For heaven’s sake! What we need is a leader and deputy leader who’ve got life experience themselves, who understand people from different classes. Because the way we’ll win an election is not just by representing one class of society, but a coalition of classes – with policies that will enhance the lives of everyone.”

Alison McGovern, the Wirral South MP and chair of the Progress group of Labour centrists, said: “Actually, the candidates are pretty similar – they are all from fairly working-class backgrounds but have lived fairly middle-class lives. And let’s be honest, Keir is quite a bit older than the others, so he’s going to have more wealth built up – that’s just a fact.”

Elections experts say the class background of a leader makes little difference to voters. Paula Surridge, a senior lecturer in political sociology at the University of Bristol, said: “I don’t know how anybody can come to the conclusion that you need a working-class Labour leader, having just lost an election to Boris Johnson. The voters want somebody who they feel shares their values, which doesn’t have to mean someone who shares their life experiences.”

Tim Bale, who runs the party members project at Queen Mary University of London, said: “As far as the electorate is concerned, everything we know about working-class people generally is they’re not averse to someone who’s bettered themselves and climbed out of the working class.”

Surridge said there was too much focus in Labour on an outdated concept of what working class means, involving manual labour in traditional sectors.

“People tend to talk about mining and heavy industry, rather than shops and care homes and hairdressers – the jobs that working-class women have been doing for decades,” she said. “It’s a very gendered conception of class; it’s a conception of class that writes working-class women out very, very quickly.”

Clive Lewis, the leftwing MP who dropped out of the leadership race this week, said the scrutiny of candidates’ life stories reflected a quest for authenticity.

“Clearly, whether Keir has an Aga or whether Emily Thornberry has the chandeliers cleaned at her house is irrelevant, politically,” he said. “A lot of it is a fetishisation of class politics into these niche little shorthands as to whether you’re authentic or not. It’s really about authenticity: am I being duped? People are striving for a kind of truth, in an era of cynicism.”

Stewart Wood, a former adviser to Ed Miliband, who was pilloried for having two kitchens, said a leader’s politics also made a difference to how they were perceived by Labour colleagues.

“The Labour party has always been massively contradictory. Tony Benn never got a bit of grief from anyone on the left for being from a hereditary background. If you have the right ideology, it washes your sins away for that part of the party that also cares about class. It’s much harder if you’re from the right of the party and you’re posh, like Tony Blair.”

Many of the 60 seats lost by Labour last month across Wales, the Midlands and the north of England were in so-called “heartland” areas once dominated by mining or heavy industry, prompting a fraught debate about how to reconnect with Labour’s traditional base.

The veteran pollster Peter Kellner gave a presentation to Labour peers this week pointing out how dramatically the class makeup of the party’s support had changed over the past three decades.

He compared this general election to 1987’s, when Margaret Thatcher’s Tories won a majority of 102. Labour’s share of the vote was 32% in 1987 and 33% in 2019. But back then Labour captured 41% of C2DE voters – the traditional academic definition of working-class – whereas in 2019 it took just 33% of that group. The Conservatives took 48% of C2DE voters.

Faiza Shaheen, the director of the thinktank Class, who stood as a candidate in Iain Duncan Smith’s Chingford seat where she grew up, cautioned against drawing the conclusion that Labour had lost the working classes and needed to change direction to win it back.

“If we want to have a conversation about class then we need to not be throwing people of colour under the bus,” she said. “We’ve got to remember that the working class is multi-ethnic, it’s in the north, it’s in the south, it’s in London just as much as it’s in Durham.”

She also warned against the idea of picking a candidate because they looked or sounded like or shared a background with the voters Labour needed to win back. “Labour did really badly among white men over 70,” she said. “Guess what Jeremy Corbyn is?”