Ministers have agreed any “backstop” arrangement to prevent the return of a hard border between Northern Ireland and the Republic after Brexit should not continue for more than a year after the end of the transition period.
A Government technical note said the UK expected permanent customs arrangements to be in place by the end of December 2021 at the latest.
The move came after Brexit Secretary David Davis was reported to be considering resigning unless there was a clear time limit on the temporary customs arrangements which would be adopted if there is no final Brexit deal.
“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.”
Downing Street said earlier that Mrs May had held “constructive” talks with Mr Davis and expected him to remain in his post.
The Prime Minister also held separate face-to-face discussions in her parliamentary office with the two other leading Brexiteers, Foreign Secretary Boris Johnson and International Trade Secretary Liam Fox.
None of the three ministers threatened to resign during the discussions, a spokeswoman for the Prime Minister said.
“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.”
Under the current timetable Britain is due to leave the EU on March 29 2019 followed by a transition period running to the end of 2020.
The paper proposes that if there is no final agreement, there should be a temporary customs arrangement lasting up to 12 months.
During that period there would be no “tariffs, quotas, rules of origin (or) customs processes” applied to UK-EU trade.
At the same time the UK would be able to strike free trade agreements with other countries and to implement those elements which did not affect the functioning of the backstop.
The paper was issued after Mr Davis was believed to have insisted the UK should be able to unilaterally withdraw from any border agreement to maintain leverage with Brussels in negotiations.
Pressed on whether he could remain in post if the backstop deal did not meet his full approval, Mr Davis said on Wednesday: “That’s a question, I think, for the Prime Minister, to be honest.”
Mr Davis made it clear the document would be “decisive” as he said he planned to meet chief EU negotiator Michel Barnier again for Brexit talks next week.
The EU’s chief negotiator Michel Barnier welcomed the publication of the paper.
He said they would be examining the proposals in the light of three questions: “Is it a workable solution to avoid a hard border? Does it respect the integrity of the single market/customs union? Is it an all-weather backstop?”
Ireland’s deputy premier Simon Coveney warned that unless there was a legally-binding assurance that a hard border would be avoided “in all circumstances”, there could be no progress on other elements of the Brexit talks.
“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,” he said.
“The EU has been clear that the backstop is an essential element of the EU-UK withdrawal agreement and that negotiations can only progress as long as all commitments undertaken so far are respected in full.
“Ireland and the commission have both stressed that substantial progress on the backstop is needed before the June European Council. Clearly, a great deal of work remains to be done and this needs to be the highest priority for all sides in the weeks ahead.”