But the European Union is mounting resistance to any specific time limit being included in the text of the UK's Withdrawal Agreement, while Leave-backing ministers are understood to be insistent that the end of the arrangement should be more precisely defined than the vague term "temporary".

A Number 10 source said that the Government's position had not changed and "big issues" had yet to be ironed out.

Speaking in Brussels, Barnier said a full customs union between the United Kingdom and the EU would solve the controversial Irish backstop issue as no new checks would be needed on goods crossing the border on the island.

Trade secretary Liam Fox told friends that her proposal "would make life very hard for me", according to a Mail report, because it would limit the UK's ability to strike new free trade deals outside the EU.

Other cabinet members, who appeared to not have been invited to the meeting, including Esther McVey, the work and pensions secretary, and Penny Mordaunt, the global development secretary, were said to be frustrated with the lack of a time limit, and, according to The Times, citing an unnamed source, were considering their positions.

Several eurosceptic ministers are now reportedly considering resigning over plans to give ground on the so-called backstop arrangement.

Her proposals are reported to involve Britain remaining part of the customs union on an indefinite basis, meaning EU rules and regulations will continue to apply.

The prime minister's refusal to bow to pressure from senior ministers to put a strict time frame in place now looks likely to spark a raft of resignations. But the European Union is unlikely to back down, pointing out that the backstop provision needs to be "all-weather" to fulfill its function as an emergency measure to avoid a new border in Ireland. The party objects the backstop plan because it would effectively keep Northern Ireland in the single market for goods and therefore place a trade barrier on businesses moving goods from one part of the United Kingdom to another.

The DUP has threatened to withdraw its support for the government if it is not happy with the final Brexit deal.

Speaking to Northern Ireland journalists at her Downing Street office, May also said she expected immigration to be a significant issue in talks.

Arlene Foster, the DUP leader, said on Thursday afternoon that the prime minister could not "in good conscience" recommend such a deal and vowed to oppose it.

Mrs May chaired a meeting of the inner Cabinet on Brexit progress Mrs May set out in June proposals for a "temporary customs arrangement" to ensure that the border between Northern Ireland and the Republic remains open in the case that no broader EU/UK trade agreement has been finalised.

While highlighting the DUP's confidence and supply agreement with the Conservative government at Westminster, Mr Coveney warned of an "imbalance" being created in Northern Ireland politics.

Theresa May's week has been hellish, but next week could be even worse.

May hopes British negotiators can strike a deal over the weekend, which she can discuss with the cabinet on Tuesday.

While London wants to regulate that by a future trade deal with the European Union, the bloc insists on an emergency fix in case negotiating new relations takes longer, or fails.