Labour is prepared to sign up to a Brexit deal with the government without the promise of a referendum attached if cross-party talks make significant progress in the coming days, one of the party’s negotiators has said.

With talks set to resume on Monday, Rebecca Long-Bailey, the shadow business secretary, made clear that if Labour’s Brexit demands were met, she would not expect the party to insist it be put to a public vote.

“Our party policy has always been that firstly we want to get a Brexit deal that puts our economy and living standards first and protects our environmental protections, workplace protections, health and safety standards,” she said.

“If we don’t get a deal that satisfies those objectives – if it’s a damaging deal, a damaging Tory Brexit deal, or there’s a risk of us moving towards a no deal – in that circumstance, we’ve said that all options should be on the table, and that includes campaigning for a public vote,” she added.

Her intervention came ahead of what is widely expected to be a combative meeting of Labour’s ruling national executive committee (NEC) on Tuesday, to sign off its manifesto for the European parliamentary elections.

Labour’s deputy leader Tom Watson, who sits on the NEC, made clear on Sunday that he will use the meeting to push for a confirmatory vote on any Brexit deal to be included in the manifesto – even urging Labour supporters on Twitter to lobby potential waverers.

He received unlikely support from Jon Lansman, the founder of the Corbyn-backing campaign group Momentum, who replied: “At conference we agreed: ‘If the Govt is confident in negotiating a deal that working people, our economy & communities will benefit from they should not be afraid to put that deal to the public.’ So surely we too can all agree to a confirmatory vote on any govt deal in our manifesto!”

Meanwhile, 21 of the party’s candidates for the European elections, including 11 sitting MEPs, sought to increase the pressure on the NEC, by signing a pledge to say they will push for a referendum with remain on the ballot paper, and if a ballot is called, campaign for remain.

Andrew Lewin, of party campaign group Remain Labour, said he hoped more candidates would sign up in the coming days.

“Remain voters across the country who want to defeat Nigel Farage’s Brexit party can now vote with confidence and enthusiasm for Labour candidates who have pledged to fight for our future, as members of the European Union,” he said.

Many at Westminster believe the cross-party Brexit talks, convened by Theresa May after her deal was rejected three times and due to resume this week, are destined to fail.

But Long-Bailey insisted negotiations had been productive and “gone into a lot of detail”, and hinted that the government was signalling a willingness to compromise on some issues, including workers’ rights.

“There has been movement in specific areas – we’ve had fantastic discussions on workers’ rights, for example, and the government seems quite amenable to moving towards what I’ve been asking for. We’re waiting at the moment to see if that turns into pens on paper,” she told Sky News’s Sophy Ridge.

The NEC will consider a draft manifesto, presented by Labour’s policy chief, Andrew Fisher, which is expected to stick closely to the conference policy of supporting a referendum only in specific circumstances.

However, shadow cabinet ministers keen for the party to back a people’s vote argue that Labour’s formal position changed when Corbyn whipped his MPs to support a confirmatory referendum earlier this month.

The shadow Brexit secretary, Keir Starmer, who attends the cross-party talks alongside Long-Bailey and John McDonnell, said in the House of Commons during the debate: “At this late stage it is clear that any Brexit deal agreed in this parliament will need further democratic approval.”

He was among those angered by the text of a campaign leaflet for the European elections leaked to the Huffington Post last week that failed to mention a referendum.

However, the Grimsby MP Melanie Onn, and the Stoke-on-Trent Central MP Gareth Snell, are among the backbenchers who believe any mention of a referendum will put their voters off – not least in this Thursday’s council elections. Their view is shared by several members of the shadow cabinet.