THE UK faces running out of time to secure an exit deal with Brussels after Theresa May hit further resistance from ministers over plans to end the impasse over the Irish border.

Andrea Leadsom, the Commons leader, warned the Prime Minister would not be able to get MPs to support an Irish backstop proposal that kept the UK in a customs arrangement with the EU without provision for the UK to quit it unilaterally.

The leading Brexiteer warned May she would also struggle to get a deal through Westminster if the plan does not include strict time limits on the arrangement.

The EU and UK agreed in a political deal in December last year “a backstop” was required in the Withdrawal Agreement – the divorce deal – that would guarantee an invisible Irish border in the event of no other solution being found either in a specific solution for Northern Ireland or in a broader EU-UK trade deal.

It is an insurance policy and would only come into force if the two sides fail to agree a permanent fix for the frontier, but remains the major sticking point in talks and is a key flashpoint for Tory anger at May’s plans.

Asked if she could quit the Government over the issue, Leadsom yesterday told Pienaar’s Politics on 5 Live: “I am working towards getting a deal that does not require the UK to be stuck, trapped in a customs arrangement. That’s what I’m working towards. And I’m sticking in the Government to make sure that’s where we get to in the end. And I’m absolutely determined about that.”

But she added: “I’m also very clear that I don’t think something that trapped the UK in any arrangement against our will would be sellable to members of Parliament.”

The latest intervention from the Commons leader came as fellow Cabinet minister Damian Hinds urged his colleagues not to risk a no-deal Brexit by torpedoing May’s plans.

The Education Secretary told the Andrew Marr Show: “We have to see what comes back and of course everybody is Parliament will be looking at that very closely and they need to think about, you know, what’s right for the future of our country. They also need to think about what the alternatives are.”

On the backstop, Hinds said a solution to the issue needed to be negotiated, stating: “If you have too hard a line about saying, ‘well we must just have a totally unilateral exit, or an absolutely fixed, hard end date’, it is very, very unlikely that is going to be negotiable with the other side. On the other hand, people here rightly want comfort and they should be able to have comfort and confidence that it isn’t an open-ended thing.”

May – who was hit by the resignation of pro-Remain minister Jo Johnson on Friday – is also under renewed pressure from the DUP on whom her government relies to shelve its Northern Ireland proposals.

A joint op-ed between the party’s Sammy Wilson and leading Tory Brexiteer Steve Baker yesterday warned May both sides stood ready to vote her deal down.

May is also said to be facing growing opposition from Brussels and is running out of time to seal an agreement. She had hoped to get the Cabinet to sign off on her proposals this week, but reports have said the EU had rejected her plans for an independent arbitration clause allowing the UK to quit a backstop deal on the Irish border.

On the Marr show defence chief general sir Nick Carter said the military makes “sensible contingency plans for all sorts of eventualities”, when asked about no-deal plans. Elsewhere, Brexiteer Jacob Rees-Mogg urged the PM to pay the EU £20 billion to secure a “no deal plus”.

On his blog ITV’s Robert Peston said: “If ... there is no agreement between [EU and UK officials] by Monday night, and no approval ... by Cabinet on Tuesday, the risk of a no-deal Brexit rises very, very appreciably.”