The veteran Labour politician Roy Hattersley has come out in favour of a second Brexit referendum, just days before Theresa May is expected to lose a parliamentary vote on the withdrawal agreement she reached with Brussels in November.

He said the “vast majority” of Labour members wanted the party to campaign for a new referendum if Jeremy Corbyn’s calls for an early general election to break the Brexit impasse did not materialise.

Hattersley, 86, who was a minister in the Harold Wilson and Jim Callaghan governments, will declare his support for the People’s Vote campaign in a speech in Sheffield on Saturday.

Parliamentary support for a second referendum is unlikely to be tested until after next week’s crucial vote, as campaigners weigh up the best moment to try to win over the Labour leadership.

However, Hattersley’s support will be seen as a significant intervention.

The former deputy Labour leader is expected to tell Corbyn to “put out of his mind all the outdated nonsense about a socialist economy being impossible in Europe”.

He told BBC Radio 4’s Today programme on Saturday morning that “sometimes, you just have to do what is right”.

He said it was clear that no deal was the worst possible scenario and needed to be averted, and dismissed controversial claims by the transport secretary, Chris Grayling, that blocking Brexit could “open the door” to extremist political forces.

Grayling told the Daily Mail British politics would take on a different tone if the UK failed to leave the EU, predicting a “less tolerant society” and a “more nationalistic nation”.

“It will open the door to extremist populist political forces in this country of the kind we see in other countries in Europe,” Grayling said.

“If MPs who represent seats that voted 70% to leave say ‘sorry guys, we’re still going to have freedom of movement’, they will turn against the political mainstream.”

Hattersley said: “I don’t think many people would regard Chris Grayling as an expert on these matters or, indeed, on anything.”

The transport secretary’s comments came after the Northern Ireland secretary, Karen Bradley, said a no-deal exit would create a “feeling of unrest”.

Hattersley will speak alongside the former Labour cabinet minister Margaret Beckett and the Liberal Democrat leader, Sir Vince Cable, in Sheffield on Saturday. Photograph: Rex Features

She told BBC News Northern Ireland: “I have been clear that I believe no deal is bad for the United Kingdom, it’s bad for the whole United Kingdom because it does put in jeopardy some of those constitutional arrangements.”

The former Irish taoiseach John Bruton told the Today programme the border backstop arrangement, which the Democratic Unionist party wants removed from the withdrawal agreement before it will support it, could not be dropped. He said it would be like Ireland cancelling its insurance policy.

Quick Guide Brexit and backstops: an explainer Show A backstop is required to ensure there is no hard border in Ireland if a comprehensive free trade deal cannot be signed before the end of 2020. Theresa May has proposed to the EU that the whole of the UK would remain in the customs union after Brexit, but Brussels has said it needs more time to evaluate the proposal. As a result, the EU insists on having its own backstop - the backstop to the backstop - which would mean Northern Ireland would remain in the single market and customs union in the absence of a free trade deal, prompting fierce objections from Conservative hard Brexiters and the DUP, which props up her government. That prompted May to propose a country-wide alternative in which the whole of the UK would remain in parts of the customs union after Brexit. “The EU still requires a ‘backstop to the backstop’ – effectively an insurance policy for the insurance policy. And they want this to be the Northern Ireland-only solution that they had previously proposed,” May told MPs. Raising the stakes, the prime minister said the EU’s insistence amounted to a threat to the constitution of the UK: “We have been clear that we cannot agree to anything that threatens the integrity of our United Kingdom,” she added.

While Ireland had no say in the Brexit referendum, Bruton said, the result had an impact on the Good Friday agreement, which brought peace to the island in 1998.

He pointed out the agreement also involved a referendum in the Irish Republic, in which voters agreed to abandon the claim on the six counties in the written Irish constitution, which has existed since partition almost 100 years ago. This, he said, meant the constitution of the union between Northern Ireland and Great Britain was not threatened by the backstop, as has been claimed.

Hattersley – due to speak alongside the former Labour cabinet minister Margaret Beckett and the Liberal Democrat leader, Vince Cable, – will say later on Saturday that there is “no conceivable deal which is remotely as beneficial to Great Britain as full membership of the European Union”.

“Jeremy Corbyn promised the party that policy would be made by the membership. Conference resolutions would, he said, be implemented.

“That means he must, difficult as it may be, put out of his mind all the outdated nonsense about a socialist economy being impossible in Europe.

“The vast majority of party members now expect that when the hope of an early general election is extinguished, Labour will campaign for a people’s vote,” he will say.

He will warn that young people in the UK will “pay the price” of Brexit, while the elderly would be protected from the long-term “penalties”.

“None of us – and that includes the leadership of the Labour party – ought to waste our time talking about another renegotiation.

“Support for a people’s vote on Britain’s future grows stronger every day. If it were backed by the Labour party, and in consequence, by the progressive trade unions, the idea would be irresistible.

“The people’s vote must enfranchise the young – not because they are passionately in favour of a European future, but because the Europe we build this year will belong to them.

“The elderly – people like me – would be protected from the long-term penalties of leaving the union, or hovering half in, half out.

“We can rely for a year or two on the prosperity which is bequeathed to us by 40 years of European membership. It is the young who will pay the price if Little England rises from the dead – reduced job opportunities, a retarded rate of economic growth and investment diverted from Britain to tariff-free markets.”

The Tory former minister Anna Soubry and the Labour MP for Wakefield, Mary Creagh, will also speak at the event as part of the People’s Vote campaign’s national Day of Action.