Ministers have been told “judgement day is coming” over Brexit as the UK and EU strive for a deal within 48 hours.
Officials are trying to hammer out an agreement on the terms of the UK’s exit by Wednesday to enable EU leaders to agree it by the end of the month.
Downing Street said talks had gone on through the night but “substantial issues” still remained to be resolved.
Amid growing pressure on the PM, one Tory said MPs will be “judged at the bar of history” if they back her plans.
Mark Francois compared Mrs May’s handling of the Brexit negotiations with the fall of Singapore to the Japanese in World War Two, complaining of “one tactical defeat after another”.
A growing number of Tory MPs are warning the prime minister that her Brexit plan will not be approved by Parliament while Labour’s Brexit spokesman Sir Keir Starmer has said MPs will not allow the UK to leave without a negotiated agreement and “technically” the whole process can be stopped.
The uncertainty has been reflected on the financial markets, with sterling falling 1% against the dollar. before recovering slightly.
The UK is set to leave the EU on 29 March 2019. Negotiations are continuing on the so-called “divorce” agreement and an outline declaration on the two sides’ future relationship. The next 48 hours are set to be critical in the process.
Both sides want to schedule a special summit of EU leaders at the end of November to sign off the withdrawal deal but the EU says it will only agree to this if agreement can be reached on the issue of the Irish border.
Time is running out to put the wheels in motion for the summit.
EU member states need time to scrutinise any agreement before the gathering and the European Council’s president Donald Tusk has reportedly said a deal must be reached by Wednesday evening at the latest.
Following an update by their Brexit negotiator Michel Barnier on Monday, EU officials played down talk of a breakthrough, saying “intense negotiating efforts continue, but an agreement has not been reached yet”.
However, the Financial Times reported that Mr Barnier told EU diplomats that the text of an agreement was “almost ready” and everything hinged on whether Mrs May could muster enough political support in the UK.
A November summit is a key staging post in trying to avoid the UK leaving without a deal.
If the decision is pushed back to the next scheduled meeting in December, no-deal preparations will have to be ramped up significantly and the chances of getting it through the UK and EU parliaments will recede.
The negotiators have been burning the midnight oil in search of a deal. Talks continued to nearly 03:00 GMT on Monday and have since resumed in Brussels.
The EU said key issues remained “under discussion”, in particular over finding a solution to avoiding a hard border between Northern Ireland and the Republic of Ireland.
Downing Street said some progress had been made but the proposed Irish backstop – a fallback arrangement for avoiding border checks, which would see the UK remain in a temporary customs arrangement – had not been agreed.
Amid claims a special cabinet meeting scheduled for Monday to approve the deal had had to be postponed, No 10 said ministers would only be asked to approve the draft agreement when it was ready.
Other sticking points include EU demands for a “level-playing field” in labour regulations and environmental standards during any temporary customs arrangement, so UK firms cannot undercut their European counterparts.
Irish foreign minister Simon Coveney said it was a “very important” week for the Brexit process and the sooner the two sides bridged their differences the better.