Call from former minister comes as Theresa May suffers another resignation in protest at her Chequers plan

Justine Greening has said she believes other senior Conservative MPs also support the idea of a second referendum to end a likely parliamentary deadlock on Brexit, after she became the most high-profile Tory to endorse such a move.

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The former education secretary and remain supporter said Theresa May’s Chequers plan “in practice suits no one” and would be rejected by both remainers and leavers. A new referendum would provide “a route forwards”, she said.

Writing in the Times, the MP for Putney said the “only solution is to take the final Brexit decision out of the hands of deadlocked politicians” by letting voters choose from three options: May’s final deal, a no-deal Brexit or staying in the EU.

Greening proposed a system using first and second-preference votes to ensure the preferred model achieved more then 50% of the final vote.

Speaking later on Monday on BBC Radio 4’s Today programme, Greening said she expected other senior Tories would support the idea.

“I think what I’m saying is what everyone is seeing in parliament,” she said. Asked whether that meant other leading Conservatives would support her specific plan, she said: “Yes, I believe so.”

Also on Monday, May suffered another resignation in protest at her Chequers plan. Scott Mann, the MP for North Cornwall, stepped down as parliamentary private secretary to the Treasury, saying he could not support a “watered-down Brexit”.

“Over the coming days, weeks and months, I fear that elements of the Brexit white paper will inevitably put me in direct conflict with the views expressed by a large section of my constituents,” he said.

Greening said she thought May’s Chequers proposal was now dead. It was a “genuine, clever attempt at a compromise” but had proved to be unworkable, she said.

“Yes, because I think in practice is suits no one, and whether you’re a remainer who looks at it and thinks, actually, we’re signing up to all the rules but now we won’t be around the table to influence them, or indeed you’re a leaver, who says this doesn’t give us the clean break we want, it doesn’t keep anyone happy,” Greening said.

“I think that millions of people who voted for leave will feel that this approach is not what they voted for in the referendum in 2016. The basic problem we’ve got is that Westminster works on party lines, but Brexit is above party politics, and so in a way it’s not set up to deal with this issue.”

What was needed was “a clear route forward that settles this European question once and for all”, Greening said. “We have to be pragmatic now about the fact parliament will not be able to take a decision on this final deal.

“I don’t believe what we need is more time. What we need is a proper decision that we can follow through on as a country.”

The idea was dismissed by Bernard Jenkin, a hardline pro-leave Tory MP. “It’s a little ill-thought out, I’m afraid,” he told Today. “If we wanted to extend the uncertainty for another long period, this is one way of doing it.”

He said the solution to the deadlock was more MPs supporting his view of Brexit. “It is stalemated because the elected politicians are, some of them, refusing to implement the decision that was taken by the British people,” Jenkin said.

Given that parliament could not agree to May’s plan, he continued, a no-deal Brexit based on WTO rules should be looked at. Challenged on the strong opposition to this from business groups, Jenkin said: “Well, businesses are lobbying for their bottom lines and their profits.”

Greening’s move has already been seized on by campaign groups seeking a second referendum, as well as by the Liberal Democrats, who said the comments “show that the sensible MPs in the Conservative party recognise the chaos wrought by a divided government”.

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Unhappiness from the Tory right over May’s proposed Brexit deal, and their threats to vote it down when a promised meaningful final vote is held in parliament around the turn of the year, have prompted growing speculation that the prime minister may struggle to ensure that whatever she negotiates will be approved by MPs, placing Britain’s future relationship with Europe in limbo.

Other high-profile figures have started to use the belief that there is political deadlock to advance arguments for a second referendum. On Sunday, Tony Blair said in a post on the website for his Institute for Global Change that there should be another national vote, because there would be no House of Commons majority for May’s Brexit, a no-deal Brexit or for remaining in the EU.

Blair also suggested there should be three choices for voters. “The question may be complicated because it really involves three choices: Clean Break, ‘soft’ or stay. But the complexity is not insuperable,” he said.