"As President Trump has said, I'm a tough negotiator", she wrote.
"The agreement contains no plan to protect our service industry and no plan to prevent a hard border in Northern Ireland, and also puts forward the idea of "regulatory flexibility", which we all know is code for deregulation of our economy".
May's position was further undermined by Trump who said in an interview published in Rupert Murdoch's Sun newspaper on Friday that her proposals would probably "kill" any chance of a post-Brexit trade deal with the US.
Before the blueprint was published, Brexit Secretary David Davis and Foreign Secretary Boris Johnson resigned, saying it would not deliver the Brexit people had voted for in the 2016 European Union referendum. "This Government will never stand for that", she said.
"But this solution - half in/half out - won't work, won't end the argument and will simply mean a confused outcome in which we continue to abide by Europe's rules whilst losing our say over them. That is unacceptable to any government here in the United Kingdom", she said.
In Edinburgh, thousands of people marched through the city in a demonstration against the US President and waved placards as they gathered in the Scottish capital's Meadows, where two giant nappy-clad baby Trump balloons were inflated.
England World Cup stars make their way back home from Repino base
Zlatko Dalic's side beat England 2-1 in Wednesday's semi-final to book a place in the showpiece for the first time. England's World Cup squad have begun the long journey back home after leaving their Repino base on Sunday.
The Prime Minister acknowledged that there were strong feelings regarding the terms of Britain's withdrawal from the EU.
The Prime Minister has warned Tory rebels they could be left with "no Brexit at all" unless they fall into line..
Mrs May denied that Mr Davis, the former Brexit secretary, had been "cut out" of the plan and therefore had no choice but to resign. "Discussions have been taking place for some considerable time", she said.
Asked if now was the moment for Johnson to lead the country, Bannon, who was sacked by the White House in August 2017, said: "I believe moments come". She said it for Mail on Sunday, as Reuters reports. It would remove our ability to have an independent trade policy at all, conceding Britain's role on the global stage as a force for free trade and endangering people's jobs and livelihoods.
"We need to ensure there is a balance between protection and public safety and the public's right to peacefully protest".
As Yahoo News reported, Trump claimed that he was misquoted in a now-viral interview in which he criticized the way May handled the Brexit and threatened to back out of a proposed trade deal with the U.K., even after claiming that a new trade deal with the United States would be a major benefit of the U.K. leaving the European Union.