She told Parliament that in the past three weeks agreement had been reached on everything from the status of the British Overseas Territory of Gibraltar on the European mainland to security cooperation with the EU.
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.
There is also the concern about the longevity of a UK-wide solution as a means to preventing a hard border in Northern Ireland.
The Prime Minister told MPs she could not accept the EU's original backstop plan as it would mean imposing controls on goods traded between Northern Ireland and the rest of the United Kingdom, creating "a customs border down the Irish Sea".
Irish broadcaster RTE reported that the European Union is ready to agree the UK-wide backstop proposed by Mrs May, but only as part of a separate treaty following a withdrawal agreement including a backstop applying to Northern Ireland only.
Other Labour and Conservative MPs believe that voting against the deal could allow them to table amendments which they could use to push for a softer Brexit or force the government to legislate for a fresh referendum.
May said the EU had shifted and was "actively working with us" on a British counter-proposal that would keep the whole U.K.in a customs union with the bloc. Brussels is now considering this but has not been prepared to accept the proposal so far.
The former Brexit secretary, David Davis, touted by some as a successor to May, wrote in The Mail on Sunday that "even the most charitable verdict on last week's Brexit talks in Brussels can hardly describe them as a success", because May appeared to endorse extending the transition period beyond December 2020.
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"It seems to me that by saying the transition would only be extended by a few months, it could be a sign that the government is reverting to its original position, in which it had initially offered a transition period of two years".
She said that electricity, telecommunications, energy, the environment, and broadcasting are just some of the areas that would need "specific arrangements for to sustain after withdrawal" from the EU.
The PM will tonight give a speech to the 1922 Committee of backbench Tory MPs where she will aim to shore up her support and see off threats to her leadership.
"It is more likely to negotiate a reversal from Brexit in 36 months than 3 months", Lamberts, who meets on a weekly basis with the EU's chief Brexit negotiator Michel Barnier, said in an interview with BI.
Ever since losing her party its majority in parliament with a botched bet on a 2017 snap election, May has faced talk of a leadership challenge.
Technicals indicated sterling had fallen below its 55-day moving average - closing below this level would signal more downside risks, chartists said.
Mrs May's usually meets on Tuesday and there is now high tension around the Cabinet table. "The fact that we aren't and that we have stood up for ourselves has made some of them quite annoyed - but so be it", the Taoiseach said. A plan mooted in Brussels to extend the post-transition to resolve the matter added to their fears.