The turnaround was announced today (Monday), as the Prime Minister promised, during a statement to the House of Commons, to take a more "flexible, open and inclusive" approach to involving Parliament in negotiating a future relationship with the EU as she seeks to revive her Withdrawal Agreement.
And she said she would conduct further talks this week on the controversial Brexit backstop to find an arrangement to take back to Brussels that meets obligations to the people of
Northern Ireland and Ireland "in a way that can command the greatest possible support in the House".
In the statement to the House, the PM also offered a guarantee that workers' rights and environmental safeguards would not be eroded as a result of Brexit.
And she scrapped the £65 fee for EU nationals wishing to remaining in the UK with "settled status".
But opponents hit out after she announced the move, including Labour MP Stella Creasy, who called the turnaround on fees for EU citizens to apply for settled status as "extraordinary", comparing the Conservative Party to a "burglar who ransacks your house and then wants a reward for returning something".
She tweeted: "Extraordinary the Tories are now boasting they are scrapping pay to stay for EU citizens.
"It was their idea in the first place! It's like the burglar who ransacks your house and then wants a reward for returning something of sentimental value."
Meanwhile, Mrs May again voiced her opposition to delaying or halting the UK's planned departure from the EU on March 29, telling MPs she did not believe there was a majority in the Commons for a second referendum
And she refused to take a "no deal" Brexit off the table, saying the only way to do this was either to agree a deal or to revoke the Article 50 withdrawal process, which she was not willing to do.
Mrs May was addressing MPs after holding cross-party talks in the wake of the overwhelming rejection of her Withdrawal Agreement by the Commons last week.
Insisting the Government approached the talks "in a constructive spirit", Mrs May said she regretted Jeremy Corbyn's decision to boycott them.
But Mr Corbyn dismissed the talks as "phoney", telling MPs: "The Prime Minister must change her red lines, because her current deal is undeliverable."
Mrs May's statement came as Poland broke ranks with the rest of the European Union by suggesting that the Brexit deadlock could be ended by putting a five-year time limit on the
The Prime Minister emphatically dismissed reports that she was considering rewriting the Good Friday Agreement to neutralise the issue.
Irish foreign minister Simon Coveney met chief Brexit negotiator Michel Barnier in Brussels on Monday and said he received assurances that the EU remains "firmly supportive" of the
Withdrawal Agreement in full, including its guarantees of no hard border in Ireland.
Mr Barnier himself said: "We are working 27 as a team, a single team and we negotiate as one."
But Poland's foreign minister Jacek Czaputowicz signalled a different approach from Warsaw, telling the Rzeczpospolita newspaper: "If Ireland asked the EU to amend the agreement with the British on the backstop so that it would apply temporarily - let's say five years - the matter would be solved.
"It would obviously be less favourable for Ireland than an indefinite backstop, but much more advantageous than no-deal Brexit."
Mr Czaputowicz said that London and Dublin were "playing chicken" over the border and risked a "head-on collision" in which Ireland stood to "lose the most".
In her statement, Mrs May said: "I will be talking further this week to colleagues - including in the DUP - to consider how we might meet our obligations to the people of Northern Ireland and Ireland in a way that can command the greatest possible support in the House.
"And I will then take the conclusions of those discussion back to the EU.
"Spelling out the approach she plans to take to negotiations on post-Brexit relations between the UK and EU, Mrs May said: "It is my responsibility to listen to the legitimate concerns of colleagues, both those who voted Leave and who voted Remain, in shaping our negotiating mandate for our future partnership with the EU.
"So the Government will consult this House on its negotiating mandate, to ensure that Members have the chance to make their views known, and that we harness the knowledge of all select committees, across the full range of expertise needed for this next phase negotiations - from security to trade.
"This will also strengthen the Government's hand in the negotiations, giving the EU confidence about our position and avoiding leaving the bulk of Parliamentary debate to a point when we are under huge time pressure to ratify. "
And she added: "I will ensure that we provide Parliament with a guarantee that not only will we not erode protections for workers' rights and the environment but we will ensure this country leads the way."