Theresa May will go into a crunch meeting with EU leaders on Monday admitting she has yet to find a solution to the Irish border problem, as a Cabinet minister suggested for the first time that Brexit might not happen.

Mrs May has until Monday night to meet an EU deadline for Britain to make “satisfactory progress” on the issues of money, citizens’ rights and the border in order to trigger trade talks this month.

She had hoped the meetings in Brussels with Jean-Claude Juncker and Donald Tusk would be the moment when trade talks would be unlocked, but Government sources were highly pessimistic about the prospect of a breakthrough, leaving the entire Brexit timetable in jeopardy.

It came as Jeremy Hunt, the Health Secretary, told Tory rebels that if they did not back Mrs May in the negotiations “we will have no Brexit”.

With just 10 days to go until next week’s European Council summit, when EU leaders will decide whether trade talks can begin, Mrs May is rapidly running out of time to keep Brexit on track.

With no agreement in sight between London, Dublin and Belfast on the border issue, the Prime Minister is now likely to ask for a last-minute extension to the Monday deadline.