The Prime Minister will call for a compromise over talks, particularly with the Irish border issue, during a crunch summit in the Austrian city of Salzburg today.
Mrs May will brief her EU counterparts on her controversial Chequers plan.
And one ally of the Prime Minister said: “She will ask EU leaders to imagine if it was their country and there was a proposal to carve off a section of their own country.
“They may understand that problem more than a technocrat in Brussels.”
It comes as Frenchman Mr Barnier hinted he was ready to make the first move in concluding gruelling talks on the Irish backstop that have plagued Brexit negotiations since the June 2016 referendum.
Speaking last night he claimed the bloc is “ready to improve” its Irish border proposal before warning the October EU summit will be the “moment of truth” for Brexit negotiations.
He said: “We are now on the home straight.”
But a Whitehall source has told The Times Mrs May is preparing to reject the offer as she travels to Salzburg for a crunch summit with EU leaders.
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Frenchman Mr Barnier has announced he is ready to make the first move
4.02 update: Welsh First Minister calls for General Election if Brexit is rejectd in Cardiff and Edinburgh
Welsh First Minister Carwyn Jones said there should be a General election if Theresa May’s Brexit deal is rejected by devolved assemblies in Cardiff or Edinburgh.
Mr Jones said rejection of a Brexit deal by the Welsh or Scottish parliament could also be the trigger which eventually leads to a second referendum.
Wales voted to leave the EU by a margin of 52.5 percent to 47.5 percent in the 2016 referendum, though recent polls have suggested a swing towards remain.
Mr Jones told BBC Wales: “The next step is to see whether a deal can be supported by, for me, parliaments plural: Westminster, Edinburgh and Cardiff.
“If that doesn’t happen, then I don’t see any alternative other than a general election where Brexit would be the main issue.
“If there’s an inconclusive result as a result of that general election, well, how then do you resolve the issue without going back to the very same people who took the decision in the first place?
“I think at that point you are talking about the potential for a second referendum.”
3.38pm update: Tusk accuses European leaders of migrant crisis “rhetoric”
Donald Tusk has accused EU leaders of “aggressive rhetoric” towards migrants and said member states needed to stop playing a “migration blame game”.
He said: “Despite aggressive rhetoric, things are moving in the right direction, mostly because we have been focussed on external border control and cooperation with third countries which has brought down the number of irregular migrants from almost 2 million in 2015 to fewer than 100,000 this year.
“In fact, this is less than in the years before the migration crisis.
“Instead of taking political advantage of the situation, we should focus on what works and just get on with it.
“We can no longer be divided into those who want to solve the problem of illegal migrant flows and those who want to use it for political gain.
“Tonight I will ask for support for our efforts to intensify cooperation with North African countries and the idea of calling an EU league of Arab States summit in Egypt in February next year.”
3.20pm update: Raab demands clarification on Labour Brexit policy
Dominic Raab has written Labour Brexit spokesman Sir Keir Starmer demanding urgent clarification on whether it backed call for a second EU referendum.
He wrote: “I am writing to you to seek urgent clarification on Labour’s Brexit policy, following developments over the weekend which suggest your party is moving towards a position of suspending Article 50 and delaying Brexit to hold a second referendum.
“More than two years on from the referendum, with the right deal within our reach, the vast majority of British people will see that instead of trying to make Brexit a success, Labour are only interested in trying to frustrate the process.”
London’s Labour mayor Sadiq Khan has called for another referendum and described Theresa May’s handling of negotiations as “mired in confusion and deadlock”.
2.45pm update: Donald Tusk anounces another EU summit after source reveals PM will reject Brussels offer
European Council President Mr Tusk said he would call an extra Brexit summit of EUleaders around mid-November to finalise a deal with Britain.
He said: “The Brexit negotiations are entering their decisive phase. Various scenarios are still possible today but I’d like to stress that some of Prime Minister May’s proposals from Chequers indicated positive evolution in the UK’s approach.”
Mr Tusk said that went for the UK’s readiness to work closely with the EU on security and foreign policy after Brexit but stressed that Chequers proposals from Theresa May for the future Irish border and economic co-operation between the EU and Britain “will need to reworked and further negotiated”.
He added: “Today there is perhaps more hope but there is surely less and less time.
“Every day that is left we must use for talks. I’d like to finalise them still this autumn.” he said.
Donald Tusk said on Wednesday he would call an extra Brexit summit
1.15pm update: Gove ‘optimistic’ about Brexit
Brexiteer Michael Gove said he is “optimistic” about the Brexit process ahead of Theresa May’s speech with EU leaders to support her Chequers plan.
Asked if he thought the latest offer from the EU on Northern Ireland was going to progress the talks, the Envirornment Secretary said: “I’m a stubborn optimist, I’m glad EU leaders are talking, I’m glad they’re hearing from our Prime Minister and I hope we will get a good deal at the end of the process.”
His words come after a government source said the Prime Minister was going to reject the EU’s new offer on the Irish border.
12.30pm update: PM to reject ‘improved’ offer from EU on Irish border
A government source has told The Times that Prime Minister Theresa May is going to reject a so-called “improved” offer from Brussels on the Northern Ireland border.
Michael Gove said he is “optimistic” about the Brexit process
12pm update: Minister hints at second referendum Chequers plan be rejected by Commons
Treasury minister Mel Stride appeared to suggest that there was a possibility of a second EU referendum if Theresa May’s Chequers proposals are rejected by the House of Commons.
Mr Stride suggested that fear of a second poll would bring rebellious Brexiteers into line when MPs come to vote on any deal, while Tory Remainers would back Chequers to avoid a no-deal outcome.
He told Sky News: “When we have a firm deal on the table, I suspect that those to the right of the party – the pro-Brexit wing – will be very concerned that if that deal does not prevail, they will end up in the situation where we could have a second referendum or we could end up not leaving the EU altogether, so there is a danger of that happening if Chequers does not prevail.
“I think those on the other end of the spectrum will equally be very concerned that if Chequers does not prevail, we could end up in a no-deal situation.”
Mel Stride appeared to suggest that there was a possibility of a second EU referendum
11.30am update: Juncker gives Barnier affectionate kiss at pre-Brexit meeting
European Commission President Jean-Claude Juncker gave pal Michel Barnier an affectionate embrace at a pre-Brexit meeting in Brussels this morning.
The pair met to discuss the conduct of negotiations at today’s EU summit where Theresa May will brief her EU counterparts on negotiations and plead with them to back her Chequers proposal.
She will have just ten minutes to issue her speech.
Jean-Claude Juncker gave pal Michel Barnier an affectionate embrace
10.55am update: House prices climbed at slowest annual rate since Brexit
The Office for National Statistics (ONS) said British house prices rose at the weakest annual rate in nearly five years having slumped in the biggest drop in London house prices since 2009.
The climb is the latest sign of a slack housing market since the 2016 Brexit vote.
UK house prices have grown at their slowest pace since August 2013, the ONS report said.
It added the pound has jumped above $ 1.32 for first time since late July.
British house prices rose at the weakest annual rate in nearly five years
10.15am update: DUP rejects Barnier’s bid to solve the Irish border riddle
DUP Deputy Leader Nigel Dodds has blasted Eu chief negotiator Michel Barnier’s bid to “de-dramatise” the Irish border riddle as a non-starter.
Mr Dodds told the Belfast Telegraph: “So Michel Barnier says he can do different kinds of checks between Northern Ireland and the rest of the UK as if that makes it more palatable.
“The fundamental point is that internal UK checks are only needed if it is intended to separate Northern Ireland from Great Britain.
“Despite the talk of “improvements” the backstop being insisted upon by the EU would mean a different regime for Northern Ireland compared to the rest of the UK” he said.
The DUP have rejected the EU’s bid to solve the Irish border riddle
“It still means a border down the Irish Sea although with different kinds of checks. The fact is that both Theresa May and the Labour Party have said no British Prime Minister could accept such a concept. It is not just unionists who object.
“And anyone with the desire to see our economy prosper will not want to see barriers put in the way of sales to and from our biggest market in the rest of the UK.
“There is however one upside in all of this. Having dismissed technology as magical thinking for the border between the Irish Republic and Northern Ireland it is suddenly okay for the border between Northern Ireland and the rest of the UK. Progress of sorts!”
The EU has insisted on a “backstop” proposal where Northern Ireland would remain in the customs union in the event of the two sides failing to reach an agreement.
9.50am update: ‘Totally unacceptable’ Theresa May blasts EU proposals on Irish border ahead of crunch summit
Theresa May has blasted EU plans for the Northern Ireland border as “totally unacceptable” hours before she is set to make a plea to her counterparts to back her Chequers proposal.
Ahead of arriving in Salzburg in Austria for the crucial summit of EU leaders, she appeared to have already dismissed Brussels’ offer which could have paved the way for an agreement.
Mrs May said: “No side can demand something totally unacceptable from the other, such as an external border between parts of the UK.”
9.45am update: David Davis warned PM on ‘pressure point’ in late negotiations
Former Brexit secretary David Davis said he repeatedly warned Theresa May there would be a “pressure point” late in Brexit negotiations.
He said: “Always the case with the European Union is they move at the last possible minute – after they’ve tested your mettle, after they’ve taken you to the cliff edge, and that’s what will happen.”
Mr Davis spoke on BBC Radio 4 as the Prime Minister made her way to Salzburg for a crunch EU summit today.
9.35am update: Theresa May relaunches jaunty cartoon to sell Chequers on Facebook
Theresa May has used Facebook to relaunch a cartoon to sell her Chequers deal to the masses.
The six minute-long animation is narrated by Mrs May, yet she fails to make an appearance in the video which features drawings of boats and tractors.
The video was launched two months ago in an attempt to explain her Brexit conundrum using phrases like “common rule book” and “maintaining shared security capabilities”.
Theresa May has used Facebook to relaunch a cartoon to sell her Chequers deal
9.25am update: Barnier further hints at Irish border compromise
EU chief negotiator Michel Barnier has further hinted at a compromise over the Northern Ireland border, saying that he respects the “territorial integrity” of the UK.
In talks today, Prime Minister Theresa May will make yet another valiant effort to persuade EU leaders to back her Chequers deal.
The Chequers plan has caused much controversy among her waking cabinet and was the reason Brexit bulldogs David Davis and Boris Johnson quit.
Her Chequers plan was given the nod by her cabinet following the resignations of Mr Johnson and mr Davis.
David Davis said he repeatedly warned Theresa May there would be a “pressure point” in negotiations
9.15am update: Mrs May will have ten minute slot to deliver Brexit pitch
Theresa May has been given a tiny ten minute slot to deliver a plea to EU leaders on Britain’s future.
An EU diplomat told the Daily Telegraph she has been issued the slot over dinner this evening and the 27 EU leaders have been told to listen in silence so as not to undermine Brussels’ chief negotiator Michel Barnier.
Mr Barnier has dubbed the Prime Minister’s Chequers plan as “cherry picking” in the past.
9am update: David Davis expects “warm words” from EU leaders at Salzburg summit today
David Davis said he expected “warm words” from the EU leaders in Salzburg as they seek to ease pressure on Theresa May in the UK, but warned “they won’t give much”.
The former Brexit Secretary said Mrs May’s Chequers plan or no deal was a false choice, and predicted the EU will “pile on” extra demands on money, migration and other issues.
Mr Davis told BBC Radio 4’s Today programme: “All these things will come back and we’ll see more and more pressure, and [Mrs May] will have a deal she won’t be able to bring back to the House of Commons because it’ll be lumbered with loads of other EU demands, so she’s going to have to have something else.”
He also said he believed the EU is “softening” over the Irish border issue.
The former Brexit Secretary said Mrs May’s Chequers plan or no deal was a false choice
8.25am update: ‘They made that choice’ PM takes swipe at second referendum campaigners
Theresa May issued stark warning that demands for a second EU referendum risks shattering trust in Westminster.
She said: “We gave people the opportunity to make a choice. They made that choice.
“If we as politicians want people to trust us, then we have to deliver for them on that.”
Her remarks come after relentless campaigners for a second EU referendum have set out a roadmap to obtain a “People’s Vote” giving the public the final say on the outcome of Brexit negotiations.
In a report published as Mrs May made her way to Salzburg for today’s EU summit it suggested suggested the Prime Minister could be forced to concede a second referendum by a vote of MPs in Parliament.
The document also insisted the option of remaining in the EU “must be on the ballot paper”.
Theresa May took a swipe at People’s Vote campaigners
8.15am update: ‘Brexit plan DELIVERS freedoms people voted for’ says Mrs May
Theresa May has said Brexit will give Britain the “freedom to deliver the British dream”.
In an exclusive interview with the Daily Express, the Prime Minister delivered her most optimistic vision yet of how breaking free of Brussels will benefit the whole the country.
Mrs May said: “Brexit gives us the opportunity to build a better future and to help people to realise the British dream.”
Mr Barnier says he is open to operational backstop
8am update: Barnier says he is open to operational backstop
Expanding on last night’s comments Mr Barnier last night said: “We are ready to improve this proposal. Work on the EU’s side is ongoing. We are clarifying which goods are arriving in Northern Ireland from the rest of the UK would need to be checked and where, when and by whom these checks could be performed.
“We can also clarify that most checks can take place away from the border at the company premises or in the markets.
“We need to de-dramatise the checks that are needed. These checks are caused by the UK’s decision to leave the EU, its single market and the customs union.
“What we need in the Withdrawal Agreement, is a legally operational backstop which fully respects the territorial integrity of the UK.
“This backstop will only apply until a better solution is found in the context of our future relationship.”
He later added: “We are working to improve our proposal. You have got to remember that the problem in Ireland, in the light of the long and positive history of the Good Friday Agreement, and the cooperation of both sides and the Common Travel Area.”