The prime minister appeared to have avoided a full-blown Brexit crisis and an explosive cabinet resignation after a “constructive” discussion with David Davis on Thursday morning.
It followed speculation her Brexit secretary was ready to quit the government over the details of the backstop proposal.
Mrs May also held separate face-to-face meetings in her parliamentary office with Foreign Secretary Boris Johnson and International Trade Secretary Liam Fox.
The government later published its proposal for a backstop plan to avoid a hard border on the island of Ireland, with an ambition for it to end by the time of the next general election.
This will see the UK retain parts of the EU’s customs union in the event of a wider UK-EU agreement finding no solution to the issue; but Brexiteers had become concerned as to whether the proposal would truly be “time-limited”, as promised.
The Cabinet Office document states: “The UK is clear that the temporary customs arrangement, should it be needed, should be time limited, and that it will be only in place until the future customs arrangement can be introduced.
“The UK is clear that the future customs arrangement needs to deliver on the commitments made in relation to Northern Ireland.
“The UK expects the future arrangement to be in place by the end of December 2021 at the latest.
“There are a range of options for how a time limit could be delivered, which the UK will propose and discuss with the EU.”
Another paragraph clearly states the temporary customs arrangement will be “time-limited” and will come into force after the Brexit transition period ends in December 2020.
The document also states the UK will be able to “negotiate, sign and ratify” free trade agreements with non-EU countries while the backstop is in place.
And the paper adds a temporary arrangement “could only be provided in law” if an EU-UK divorce deal and a future partnership framework are agreed.
The EU’s chief Brexit negotiator Michel Barnier welcomed the publication of the UK proposal but said Brussels would “examine it with three questions”.
These were whether it is a “workable solution” to avoiding a hard border, whether it respects the “integrity” of the EU’s single market and customs union”, and whether it is an “all-weather backstop”.
The Republic of Ireland’s deputy prime minister Simon Coveney said he looked forward to discussing the UK’s proposal with Mr Barnier’s team.
Claiming there is “clearly a great deal of work” remaining to be done in Brexit negotiations, Mr Coveney said: “Our strong preference remains an overall EU-UK future relationship which would resolve all issues.
“However, it remains vital that a legally-binding backstop is agreed to provide certainty that, in all circumstances, a hard border will be avoided.”
In a morning of speculation at Westminster, Mr Davis’s chances of resigning – and delivering a damaging departure from Mrs May’s cabinet – had earlier been judged at “50-50” by a source close to the Brexit secretary.
Tory MP Nadine Dorries had also ramped up the political drama by citing Mr Davis’s SAS training, as she warned he is “trained to survive” but also “trained to take people out”.
After his talks with the prime minister, allies of Mr Davis immediately claimed victory by insisting “much more detail” would be provided on the time-limited nature of the government’s backstop proposal.
A source close to Mr Davis said: “Obviously there’s been a back and forth on this paper, as there always is when the government publishes anything.
“The backstop paper has been amended and now expresses, in much more detail, the time limited nature of our proposal – something the prime minister and David Davis have always been committed to.”
Following his around half hour-long meeting with Mrs May, Number 10 revealed the prime minister expected Mr Davis to remain in his position.
The cabinet agreed the new backstop plan last month, but Brexiteers recently became concerned it would leave the UK closely-aligned to the EU as a default long-term solution without a clear time limit.
Labour’s shadow Brexit secretary Sir Keir Starmer characterised Thursday’s events as “another embarrassing day for the government”.
He said: “The clock is ticking on the Brexit process and it is imperative that an agreement is struck which will protect jobs, the economy and ensure there is no hard border in Northern Ireland.
“Instead, with the threat of a cabinet resignation, Theresa May has signed up to a flawed proposal which is inconsistent with her earlier commitments.
“The prime minister should urgently rethink her decision and back Labour’s call for a new comprehensive customs union and new deal with the single market after Brexit.”
Fellow Labour MP Chris Leslie, who supports a referendum on the final Brexit deal as part of the People’s Vote campaign, said: “This would be laughable if it weren’t so serious.
“After weeks of the Government negotiating with itself, the fudged document they have produced doesn’t engage with any of the key Brexit dilemmas and is highly unlikely to lead to anything but more gridlock in the ongoing talks with the EU.”
Earlier this year, Mrs May rejected the EU’s own proposed backstop solution to the Irish border issue.
Brussels had suggested effectively keeping Northern Ireland in a customs union with the bloc in the event a UK-EU agreement didn’t prevent a hard border.
But, under pressure from her DUP allies at Westminster, the prime minister dismissed the plan, explaining it threatened the “constitutional integrity” of the UK.
Mrs May faces an EU summit on 28 June, at which both sides were hoping to demonstrate progress in the Brexit negotiations.
The pressure of Brexit will not ease on Mrs May before the Brussels meeting, with it confirmed MPs will consider House of Lords amendments to the EU Withdrawal Bill on Tuesday and Wednesday next week.
Peers inflicted 15 defeats on the government’s flagship Brexit legislation, which has set up a series of crunch votes in the House of Commons.
Andrea Leadsom, the leader of the House of Commons, also revealed on Thursday the government’s trade bill, which may also prompt a Brexit rebellion by pro-Remain Tory MPs, will return to the lower chamber “by mid-July at the latest”.
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Labour branded the government’s handing of key legislation a “shambles”, with shadow leader of the House of Commons Valerie Vaz highlighting how the party had asked for four days of debate for the EU Withdrawal Bill.