He told BBC Radio 4’s Westminster Hour: “Time is running out, there is no doubt about that. In all member states, preparation for all eventualities are ramping up quite significantly.”

The special EU summit pencilled in for November to sign off a Brexit agreement could instead end up being used as an emergency meeting to discuss “no-deal” plans.

Talks will take place on Monday between DUP leader Arlene Foster and Taoiseach Leo Varadkar, while Mrs May will meet Sinn Fein leader Mary Lou McDonald in Westminster.

The febrile atmosphere in the Tory ranks has seen former Brexit secretary David Davis emerge as a potential successor to Mrs May.

Tory MP Nadine Dorries publicly suggested he could be the leader to deliver the kind of Brexit sought by Eurosceptics.

The Prime Minister’s critics believe the threshold of 48 Tory MPs calling for a no-confidence vote could be passed by Wednesday, depending on events in Brussels.

Allies of Mr Davis said he has been contacted by several Tory MPs urging him to run for the leadership and he is understood to be prepared to take part in a contest.

Ms Dorries backed Mr Davis for the top job, saying: “Getting May out and him becoming an interim leader may be the only way to deliver Brexit and FTA (a free-trade agreement).”