Replying to Mrs May's statement, Labour leader Jeremy Corbyn said there have been "20 wasted months" since the European Union referendum in which the "arrogance" of some of the Cabinet who said it would be the "easiest deal in history" has turned into "debilitating infighting".
Mrs May is hoping to get a post-Brexit transition period signed off at the European Council summit of EU leaders on March 22-23, clearing the way for exploratory talks on trade. Speaking to parliament, Theresa May said that can not agree with the draft, adding that she would say this "crystal clear" to the EU.
"I am optimistic it will happen".
May, battling to strike a deal with Europe that appeases both sides of her deeply divided party, used a speech in London on Friday to warn that the country needed to face up to some "hard facts" that "neither of us can have exactly what we want".
The EU wanted to hear Theresa May utter some hard truths about the costs of Brexit and in her speech at Mansion House she tried to oblige.
But in a bid to maintain "as frictionless as possible" trade in goods, May promised to commit to some regulations and minimum standards, while reserving the option for Britain to diverge. Trade barriers would be especially damaging to Britain's fresh-food retailers, who rely heavily on the unencumbered movement of perishable goods throughout the EU.
An official in May's office told reporters the speech showed the prime minister is being pragmatic rather than theological.
She also acknowledged the "hard fact" that even after the United Kingdom leaves the jurisdiction of the European Court of Justice, EU law and the decisions of the ECJ will continue to have an impact.
But a second European Union official said: "The comprehensive system of mutual recognition she talks about won't work for us - or for that matter lead to frictionless trade".
"Now we do have an opening negotiating position".
Mr Corbyn said the UK's proposed solution to avoiding the return of physical infrastructure on the Irish border, based on what he said was a "mixture of goodwill and technology", was no more than blue-sky thinking.
"Given the importance of financial stability, of ensuring the City of London, we can't just take the same rules without any say in them", May said. "We would have to abide by their rules which were being set elsewhere".
May's speech did offer some proposals to solve some of the thorniest problems thrown up by Brexit, especially over Ireland, after the EU set out in a draft withdrawal agreement a backup plan that effectively would see Northern Ireland remain part of the EU's customs union.