THERESA May today ruled out a second referendum on Brexit - warning that it would destroy the public's trust in politics.
After 700,000 activists marched through London calling for a so-called "people's vote", the PM insisted she will respect the result of the Leave vote from 2016.
And she said a second referendum would actually be a "politicians' vote" which would show the public their views are not respected.
In a Commons statement this evening, Mrs May also called on Brits to "hold our nerve" in order to win the "prize" of a deal with Brussels - as she unveiled her four-point Brexit plan.
The PM faced demands from pro-Remain MPs for a second referendum in the wake of Saturday's demonstration.
Mrs May hit back at Tory colleague Sarah Wollaston, saying: "We gave the people a vote on this issue, there was a people's vote and people voted in larger numbers than they had done before and they voted to leave the European Union.
"I know she, like me, will be concerned about ensuring that the people actually can have some faith in our politicians, and that means our politicians delivering on the vote of the people and not telling them to think again."
Dubbing the proposal a "politicians' vote", the PM said it would mean "politicians telling the people they got it wrong the first time and should try again".
After the PM told Sun readers today that she WILL push through her exit plans - even if it means losing her job - she insisted that a deal is in sight.
As she faces threats to boot her out of office, today she stressed that there HAS been progress in the last few weeks, even though EU leaders didn't sign off a deal last week at a Brussels summit.
Mrs May told MPs in the Commons this afternoon: "95 per cent of the Withdrawal Agreement and its protocols are now settled.
"There is one real sticking point left, but a considerable one, which is how we guarantee that - in the unlikely event our future relationship is not in place by the end of the Implementation Period - there is no return to a hard border between Northern Ireland and Ireland."
But again she insisted that she cannot accept the EU's plans to put a border in the Irish sea.
She said: "As I set out last week, the original backstop proposal from the EU 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."
"I do not believe that any UK Prime Minister could ever accept this. And I certainly will not."
Instead, the PM laid out a four-point plan to guarantee that Ireland will not get a hard border and Northern Ireland will never be carved out from the rest of the UK.
She confirmed proposals for a new "legally binding" backstop that would keep the whole country in the EU customs union if there is no alternative solution to the Irish border question - as well as a possible extension to the post-Brexit transition period.
What is Theresa May’s four-point plan to save Brexit?
1) Persuade the EU to accept a UK-EU joint customs union
This would be a temporary measure for making sure that Northern Ireland was not cut off from the rest of the UK in any circumstances. The PM told MPs it would make sure there was no return to a hard border.
2) Extending the transition period
The PM said she’s not committed to it yet, but accepts that the impasse means it might need to happen. That would mean businesses only needed to change their rules once as we exit the EU.
3) Make a get-out clause from the backstop and transition period
Just in case we get tied into the EU, the PM wants us to have an option to end the agreement. She said we would have to be out “well before the end of this Parliament” which is scheduled to end in 2022.
4) Allow Northern Ireland’s trade to flow without blocks
The PM said she wanted to make sure that she protects the links between Northern Ireland and Great Britain.
But she insisted the backstop would need to be temporary - saying: "We would not accept a position in which the UK, 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."
Mrs May concluded: "Before any decision, I ask - how do I best deliver the Brexit that the British people voted for?
"The Brexit talks are not about my interests. They are about the national interest – and the interests of the whole of our United Kingdom.
"Serving our national interest will demand that we hold our nerve through these last stages of the negotiations, the hardest part of all.
"And it will mean focusing on the prize that lies before us: the great opportunities that we can open up for our country when we clear these final hurdles in the negotiations."
Earlier today one of Mrs May's key allies warned that Leave would smash Remain by an even bigger margin in another Brexit referendum.
Northern Ireland Secretary Karen Bradley said the people had already spoken, adding: “We had a people’s vote.”
Ms Bradley, who voted Remain in 2016, insisted a second referendum would undermine the democratic process.
She said: “I personally think, from my knocking on doors, there would be a bigger vote for Leave.”
Today the PM told Sun readers in an exclusive address: "The Brexit talks are not about me or my personal futures. They're about making the right choices, not the easy ones."
She went on: "I am working closely with my counterparts in Europe to explore every possible solution to the border issue.
"Does that mean I think this negotiation will get tougher before we reach our goal? Yes.
"Do I have some long and difficult days ahead? I’m sure I do.
"I’m thinking about the prize that lies before us tomorrow; about the great opportunities the Government will help open up for you once we clear the last few hurdles."
Her Commons Statement came at the start of yet another crunch week for the Prime Minister.
Rebels say they are just a few letters away from the 48 that are needed to trigger a no confidence vote, which then could result in her facing a leadership challenge before Christmas.
The PM will hold a Cabinet meeting with her top team tomorrow, while she faces demands to come to the backbench 1922 committee to try and restore faith in her MPs.
But Tory cabinet minister and Brexiteer Chris Grayling said today that now was the moment for "calm, level heads" and not to try and oust her.
The Transport Secretary told Radio 4 this morning: "The reality is that, if the deal on offer is something that can't get through Parliament, we will end up in a no-deal situation, so it is in everyone's interest, the European Union and us, to make sure that what we agree is something that both sides can accept."
Over the weekend Mrs May faced a series of anonymous briefings from furious MPs that are determined to get her out of No10, while one said she should "bring her own noose" to the meeting.
Another added that the moment was coming when "the knife gets heated, stuck in her front and twisted".
Eurosceptics were set to try and force a rebellion later this week if she continues to stick to her guns.
They were going to put amendments to Government legislation to stop Northern Ireland being placed in a different regulatory and customs territory from the rest of the UK.
But this afternoon it emerged that ex-Brexit minister Steve Baker, who was leading the charge, was ready to call off the troops because they didn't have enough numbers.
Brexiteers tell EU that Theresa May's Chequers plan won't work
A GROUP of Brexiteers travelled to Brussels today to tell the EU that Theresa May's Chequers plans won't work.
A delegation headed by ex-Tory leader Iain Duncan Smith, and ex-cabinet minister Owen Paterson, met Michel Barnier this morning, but denied they were undermining the Prime Minister.
They made their own pitch on how trade with the EU should continue after Brexit, and will advocate a fresh model.
The pair were accompanied by Lord Trimble and several trade experts too, and will say that their plan will avoid a hard border in Northern Ireland.
Mr Duncan Smith said today: "We are presenting some ideas which we think are constructive and we had a constructive discussion.
"Now we are going to go back and talk to the Government about it."
He added that whoever briefed in violent terms about the Prime Minister's future "needs to have the fullest weight of the Conservative Party upon them". "It has nothing to do with our politics, it has nothing to do with this issue," he told reporters in Brussels, adding that the Prime Minister had his "full support".
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Mrs May held a series of conference calls with ministers over the weekend to try and shore up her position.
Esther McVey, the Work and Pensions Secretary, was said to have been "devastated" at plans to increase the transition period.
Sajid Javid was also said to have warned her that there must be an end date on her customs union backstop, and Attorney General Geoffrey Cox was said to have raised significant concerns too.
One source told the Telegraph: "It raised more questions than answers."
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