THERESA May’s Brexit plans have led to further public splits in her cabinet, with one minister dismissing a colleague’s red line as “very, very unlikely” to happen.

Remain-backing Education Secretary Damian Hind said the EU would not accept the UK being able to walk away unilaterally from an Irish backstop arrangement.

However Brexiter Commons leader Andrea Leadsom said it was vital that the UK was free to leave without the EU’s permission, otherwise it could end up “trapped” in a customs union.

With rumours of multiple resignations in the coming says, Ms Leadsom also said she would be “sticking in government” to ensure her case was made.

The infighting coincided with a new poll for the pro-Remain Best for Britain group showing two-thirds of people, including most Leave voters, want another Brexit referendum.

The Populus survey of more than 8000 people found 65 per cent backed the British public “having the final say on the Brexit deal”, including 52 per cent of Leave voters.

Best for Britain chief executive Eloise Todd said: “This poll is a ground-breaking moment in the campaign to bring about a People’s Vote.

“For the first time people who voted to leave in 2016 want a vote on the final deal.”

The government’s splits over Brexit were mirrored by divisions within Labour.

On Friday, leader Jeremy Corbyn went against his party’s official, open-minded position on a People’s Vote by saying Brexit was now unstoppable.

But on BBC1’s Andrew Marr programme, shadow foreign secretary Emily Thornberry walked the comment back, insisting another Brexit referendum was possible after all.

The widening splits at the top of the government came just 48 hours after Jo Johnson, the brother of Boris Johnson, quit as Transport Secretary over Mrs May’s Brexit plans.

A Remain voter, Jo Johnson accused the Prime Minister of a “terrible mistake” and of trying to force MPs to choose between her deal and an equally unpalatable No Deal.

He said there should be a People’s Vote to decide what the nation should do next.

The Prime Minister’s problems centre on an Irish backstop guaranteeing no return to a hard border if the UK can’t agree a trade deal with the EU by the end of 2020.

The government has suggested a temporary UK-wide customs union with the EU as the way round the issue, but the EU insists there must still be an all-weather measure for Ulster.

The cabinet disagreement is over how the UK would leave such a measure.

Mrs May’s plan has suggested giving the EU a joint-say in an independent review mechanism which would assess if the customs arrangement was still necessary.

However Brexiters fear that would leave the UK stuck until the EU said otherwise, as well as under the European Court of Justice, and want the UK to be able to withdraw unilaterally.

It was reported on Sunday that the EU had rejected the "independent mechanism" proposal.

Ms Leadsom told BBC Radio 5: “I am working towards getting a deal that does not require the UK to be stuck, trapped in a customs arrangement.

“I’m sticking in government to make sure that’s where we get to in the end.”

She added: “The UK cannot be held against its will in a customs arrangement. It must be capable for the United Kingdom to decide to leave that customs arrangement and it cannot be something that the European Union can then hold us to.

“And, frankly, it’s because that would be to then fail to fulfil on the will of the people expressed in the referendum and I very much doubt that we would get it through parliament.”

But on BBC One’s Andrew Marr programme, Mr Hinds said the EU would not accept the UK alone being able to end the backstop, as that negated the essence of the insurance policy.

He said: “If you have too hard a line about saying, ‘well, we must just have a totally unilateral exit, or there’s an absolutely fixed, hard end date’, that is very, very unlikely that is going to be negotiable with the other side.”

He said there would inevitably be “trade-offs” to any deal, and so it would not satisfy all sides, and urged Tory Brexiters and the DIP to “think about the alternatives”.

But in a joint Sunday newspaper article, former Brexit minister Steve Baker and DUP MP Sammy Wilson also warned the Prime Minister her plan faced rejection in the Commons.

They wrote: “We share the prime minister’s ambition for an EU free trade agreement, but not at any price, and certainly not at the price of our union.

“If the government makes the historic mistake of prioritising placating the EU over establishing an independent and whole UK, then, regrettably, we must vote against the deal.”

On the same show, Ms Thornberry tried to reassure Labour supporters dismayed by Mr Corbyn’s rejection of a People’s Vote over the weekend.

She said Mr Corbyn's comments had to be seen in context and he was explaining that: "We had a referendum, that we are democrats over and above everything else."

She said Mrs May’s binary choice between “falling off a cliff" and a “bridge to nowhere" and Labour would not play along, and if Mrs May lost her meaningful vote in the Commons, the party would demand a general election.

She told Mrs May: “You cannot simply come to the House of Commons with a bit of nonsense that makes no sense.

"You cannot expect the Labour Party to save you from your own backbenchers who are saying this deal makes no sense - and everybody knows it doesn't make sense."

She said: “If we don't have a general election, which we think we should have, then yes of course all the options remain on the table and we would campaign for there to be a People's Vote but, you know, there are several stages before we get there."