Rebecca Long-Bailey has cemented her position as the only Labour leadership candidate who would grant the Scottish parliament the legal powers to hold a second referendum on independence, telling a hustings event in Glasgow on Saturday that refusal “would drive more of our voters into the arms of the Scottish National party”.

At the only hustings taking place north of the border, all three remaining candidates emphasised their understanding that the party can only secure a majority at Westminster if it wins back its Scottish heartlands.

Long-Bailey said: “As a socialist, I believe in collective solutions and I’m proud to be from the UK, but as a democrat, if the Scottish parliament makes the request for a referendum, I don’t believe as a democratic party we could refuse that.”

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She added: “I also know if we did refuse that it would drive more of our voters into the arms of the SNP,” before insisting that Labour could “confidently make the case for the UK” while recognising the need to devolve political and economic power out of Westminster.

Lisa Nandy used the Scottish hustings to double down on her opposition to a second referendum, saying: “We have to be absolutely clear and stand up for Scotland remaining in the UK and for solidarity across the nations and regions of the UK.”

She added: “We have to stand up to the SNP because it suits them … that the entire debate is about whether Scotland remains in the UK or not, because as long as they can divide people and provide grievance and resentment they will continue to mask their own failures on child poverty, mental health, social care, homelessness, drug deaths, all of these areas that I am outraged about.”

Long-Bailey and Nandy drew applause for their positions from the audience of several hundred Scottish Labour members, activists and politicians at the Scottish Event Campus on Saturday.

Keir Starmer, meanwhile, did not rule out the possibility of a second vote, saying: “Whether the Scottish parliament should have the power over an independence referendum is an interesting question, but we shouldn’t get sucked into that. The SNP are constantly using the constitutional issue to mask other issues.”

Following a series of damaging interventions from the UK Labour leadership last year, the Scottish branch of the party was bounced into reversing its complete opposition to a second referendum.

During the general election campaign, Jeremy Corbyn refined his position to supporting an independence vote only after two years or more of a Labour government in London. In January, Boris Johnson rejected first minister Nicola Sturgeon’s request for the legal powers required to stage a second vote.

In a hustings session that focused heavily on how the Labour party might rebuild in Scotland, the replies were largely consensual aside from when the contenders were asked if they would commit to having the other two candidates serve in their shadow cabinet if they became leader.

Starmer immediately refused to “get into jostling for position”, while Nandy and Long-Bailey indicated that they would be happy to serve with the others. Long-Bailey joked: “I feel a bit sad that Keir doesn’t want us in the cabinet!”

Questioned closely about plans for a fresh constitutional settlement for Scotland and across the UK, Starmer said: “We have got stuck between the status quo and independence. We need a radical federalism arrangement where Scotland has more powers and a different relationship with the rest of the UK.”

Pledging to “come straight back up here” if elected leader to help kickstart Scottish Labour’s campaign for the 2021 Holyrood elections, he said the party would need far stronger messaging than it had in the last election: “We have to attack the SNP on their record and not let them hide behind constitutional issues.” He added that he would bring the Scottish Labour party “much closer to the [UK] leadership”.

Promising a different style of leadership, Nandy said she wanted “to make common cause with SNP voters, not Nicola Sturgeon”.

Acknowledging that the challenge of rebuilding Scottish Labour – which polled 18.6% in last December’s election, its worst result in recent history – was “absolutely enormous”, she noted that voters in Aberdeen could still feel distant from Holyrood in Edinburgh, saying: “We give people power over their own lives by handing more power to councils.”

Long-Bailey said the party had to understand “where our votes went” both in the north of England and in Scotland.

“We can’t blame our voters for going to the SNP,” she said, before calling for “radical devolution”, including more powers to Holyrood for additional borrowing and employment rights, reflecting the recommendations of Pauline Bryan, the Corbyn ally tasked last year with writing a detailed paper on how federalism could work.