The shadow chancellor, John McDonnell, has said the Labour party will whip its MPs to back a second referendum rather than offer a free vote, a move that the senior backbencher Caroline Flint warned could lead to the rebellion of up to 70 MPs.

McDonnell said it would be common practice to see MPs whipped to support party policy, but he understood the difficulties such a decision could pose for MPs in leave constituencies.

“Normally we will whip and that will be decided in the normal way by the chief whip and the shadow cabinet and the party overall,” he told Sky’s Sophy Ridge on Sunday.

“I think on an issue as this we would see a whip but also you’ve got to respect people’s views and their constituency interests as well, and the whipping arrangement will be determined in discussion in due course.”

He said Labour would “never be forgiven in the future” if it allowed a Brexit deal or no-deal exit to damage people’s jobs and the long-term future of the economy.

A number of frontbenchers have publicly opposed a second referendum, including the shadow housing minister, Melanie Onn, and the shadow justice minister, Gloria De Piero.

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Flint urged McDonnell and the Labour leadership to allow a free vote and said she hoped Labour colleagues would vote for an improved Brexit deal including one with new promises on workers’ rights that she and other Labour MPs had been working to secure.

“Myself and so many Labour MPs in the general election 2017 made a promise to respect the outcome of the referendum and that was Labour’s policy,” she said.

“So my appeal, to Jeremy Corbyn, John McDonnell, to Keir Starmer, is to allow MPs a free vote on an improved deal, so those who want a second referendum can vote for that but those of us who want to keep our promises to our electorate can also keep faith with those people.”

McDonnell said discussions would take place in the shadow cabinet about what kind of amendment for a fresh public vote the party could support – and that frontbenchers would be expected to support it.

“In the normal way we’ll come to a conclusion on the exact wording of whatever amendment was put up and you’d expect the frontbench to support it,” he said.

Asked if he believed he was damaging Labour’s electoral prospects, McDonnell said: “It may well be but we’ve got to be honest with people – people have had enough of politicians who say one thing and actually do another.”

McDonnell also hinted he could attend the People’s Vote march on 23 March, the weekend before the UK leaves the EU. “Well, I’ll think about it certainly, I’m not one to miss a good march,” he said.

“I also have to say as well I don’t want to do anything or say anything that disrespects the people who strongly, in my own constituency and elsewhere, supported leave.”

The shadow business secretary, Rebecca Long-Bailey, echoed some of Flint’s concerns and insisted the party would not stop pushing its own version of a Brexit deal or the possibility of a general election, saying she “truly hopes” the party is not forced into backing a second referendum.

“We have got to leave all options on the table to avoid an economic catastrophe for Britain,” she told the BBC’s The Andrew Marr Show. “We are not looking to overturn the result of the referendum.”

Long-Bailey said a referendum would have a deal versus “a number of other options” on the ballot paper. Asked if that would include remain, she said that was “not in the Labour party’s gift to determine what would be on the ballot paper, it would be up to parliament to decide”.

She said parliament should provide a number of credible options to voters, including a Labour Brexit deal and a Norway-style deal that would keep the UK in the single market and customs union.

However, Long-Bailey insisted a referendum was still not the priority for the party. “That’s not the point we should be moving towards, we need a deal that will pass parliament and secure economic protection for people,” she said.

Long-Bailey said she understood Flint’s position against a referendum. “I’ve always voiced my own reservations about having a second referendum … but we can’t put Britain into an economic catastrophe,” she said.

“I truly hope we don’t get to that point … we are pushing for that Labour deal that will protect jobs and the economy.”

The breakaway Independent Group of former Labour and Tory MPs who back a second referendum have called on the party to clarify its unequivocal support for a fresh poll. The group’s spokesman, the former Labour MP Chuka Umunna, said it was time to “end the ambiguity in Labour’s position”.

In an open letter to the shadow cabinet, the group calls on the party to clarify whether frontbenchers who oppose a second referendum will be sacked – and whether the party would back a new vote even if Labour’s Brexit deal was accepted.

“All terms and conditions attached to a people’s vote need to be dropped and an unequivocal commitment given now to make it happen,” Umunna said. “There is no time to waste.”

The former Labour prime minister Tony Blair said Labour MPs who were uneasy about a second referendum should push for an extension in order to gauge the public mood.

“I think you’ll get to another referendum when people understand that a hard Brexit is going to be deeply economically painful for the country and a soft Brexit means we just become a rule-taker,” he said.

“It’s in those circumstances that I think you mobilise a majority in parliament to say the sensible thing in these circumstances is to put it back to the people, or pass her deal subject to a confirmatory referendum.”