Lisa Nandy has accused her rivals for the Labour leadership of failing to grapple with the scale of the challenge facing the party, as the candidates clashed over antisemitism, Brexit and economic policy in the contest’s first televised debate.

“The challenges we face are so big and yet the debate we are having is so small,” the Wigan MP warned, as she and Rebecca Long-Bailey, Keir Starmer and Emily Thornberry set out their pitches on BBC Two’s Newsnight.

With all four candidates adopting sections of the 2019 manifesto, policy differences have been relatively modest in the contest thus far – and some of the focus has fallen on internal party democracy.

“We are not going to win back Bassetlaw by deselecting MPs and grandstanding about military action,” Nandy said, in an apparent sideswipe at Long-Bailey’s promise of open selections for Labour candidates, and Starmer’s pledge to introduce a prevention of military intervention act (PMIA) to avoid “illegal wars”.

“People are smarter than we think. We can’t go round as a party, promising to nationalise everything, to get rid of tuition fees, when we haven’t got a clue how we would do it, or how we would pay for it.”

That comment was described as “nauseating”, by Labour’s former policy chief Andrew Fisher, who tweeted that the promises were fully costed.

Andrew Fisher (@FisherAndrew79) Nauseating to hear a candidate for Labour leadership say we were going "to nationalise everything" or that we didn't spell out how to pay for scrapping tuition fees when it was fully costed in 2017 and 2019 #Newsnight

Starmer had earlier published 10 “pledges” to Labour members. As well at the PMIA, these included retaining Jeremy Corbyn’s policies of scrapping student tuition fees and nationalising rail, mail, energy and water.

Some of the liveliest exchanges came as the candidates discussed the party’s record on antisemitism – which all four said they would apologise for.

Starmer said: “If you are antisemitic you shouldn’t be in the Labour party. And if you’re not prepared to fight antisemitism, you shouldn’t be in the shadow cabinet. This takes leadership; I’ve led a national organisation – I know that if you’re going to change an organisation, you’ve got to lead from the top.” He said he would insist on being updated regularly on cases.

“All leadership candidates will take forward a robust plan of action, very quickly,” said Long-Bailey. “We are an anti-racist party and we have to be the gold standard, and we have to recognise that over the past few years we did not tackled this issue adequately.”

At one point, Thornberry noted that she and Starmer had both raised antisemitism repeatedly in the shadow cabinet, and called for regular reports on tackling it. “I don’t think Rebecca did,” she said.

“We may be throwing antisemites out of our party now, and I’m pleased to see that we are, but why weren’t we doing that two and a half years ago?” she asked.

Long-Bailey claimed she had also spoken up, saying, “I did, I think you’ll find” – prompting Starmer to warn, “let’s not descend into scoring points.”

Brexit was also controversial. Starmer is viewed by many party members as the champion of the remain cause. But he rejected the idea that he was the “architect” of Labour’s policy on the issue, and insisted other members of the shadow cabinet, including Long-Bailey, had signed up to it at the same time.

Long-Bailey, whose Salford and Eccles constituency voted to leave, said: “I understand why Keir took the action that he did within parliament to try and avoid a damaging no-deal Brexit, but sometimes in our communities it seemed as if we were playing parliamentary games. Our message didn’t get out there, and it resulted in the catastrophe that we saw on election night.”

Starmer, Long-Bailey and Nandy have all secured their place on the ballot paper. Thornberry has until Friday to win the 33 constituency labour party nominations necessary.

Shortly before the debate was broadcast, Thornberry tweeted that she needed seven more, urging Labour members to support her, in order to, “get the widest range of voices, skills and experience on the ballot”. In her closing pitch in the debate, she described herself as a “streetfighter”, and “a campaigner to my marrow”.