And in Northern Ireland, agreements on the preservation of the particular rights for United Kingdom and Irish citizens.
The shadow Brexit secretary said the deadlock in Brussels is a "mess of the prime minister's own making" and warned she is unlikely to survive unless she gains support.
Her opponents had spent the weekend claiming they were close to gathering sufficient support to trigger a vote of no confidence in the Prime Minister, with Wednesday's meeting of the 1922 Committee of backbench Tory MPs being billed as a make-or-break moment for her leadership.
Theresa May must clarify if the proposed extension to the Brexit transition period serves as an alternative to the EU's demand for a backstop, Sammy Wilson has said.
She reported progress on some issues including in areas of security, defence and Gibraltar, noting that "95 percent of the withdrawal agreement and its protocols are now settled".
The EU proposal for Northern Ireland to remain in the bloc's customs union has been rejected by May as it would potentially create barriers to trade with the rest of Britain - something ruled out by Northern Ireland's DUP party, whose 10 votes in parliament prop up May's government.
Gibraltar, a British overseas territory located at the tip of the Iberian peninsula and regularly claimed by Spain, will leave the European Union along with the UK.
However, during her address Mrs May said: "We would not accept a position in which the United Kingdom, having negotiated in good faith an agreement which prevents a hard Border in Northern Ireland, nonetheless finds itself locked into an alternative, inferior arrangement against our will".
But she will add: "As I set out last week, the original backstop proposal from the European Union was one we could not accept, as it would mean creating a customs border down the Irish Sea and breaking up the integrity of the UK".
Image caption Simon Coveney said: "There will be no withdrawal agreement without the backstop, end of story".
Jack Blanchard for Politico writes that divisions over Brexit have turned the party into "a powder keg", with open talks of an imminent vote of no confidence against May, and "the feverish atmosphere led at least one MP to brief Sunday newspapers in, frankly, disgusting terms".
On Monday, she reiterated the position, stating that the United Kingdom might need to ask for a short extension "as an alternative to the backstop".
In order for a no confidence vote to be held, 48 letters from Conservative MPs must be submitted to the party's chairman.
As talks stall there has been proposals to extend the Brexit transition period for another year.
Downing Street told CNN it would not be commenting on Mercer's interview.
Steve Baker, a leading ERG member, has tabled amendments to government legislation which could stop Northern Ireland being placed in a different regulatory and customs territory from Great Britain without a vote in the Northern Irish parliament in Stormont.
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