The Brexit talks are on the verge of a breakthrough after Theresa May appears to have conceded to Dublin’s demands on the Irish border following a frantic weekend of diplomacy.

As the Prime Minister sat down for lunch with Jean-Claude Juncker, the European Commission President, in the Brussels, details of the draft agreement emerged.

They made reference to continued “regulatory alignment” between Northern Ireland and the Republic post Brexit, which seems to reassure the concerns of the Irish Government over maintaining the open border and close relationship between Northern Ireland and the EU.

It was suggested this wording was more acceptable to Whitehall than previous drafts, which referred to “no regulatory divergence”. This was said to openly imply full acceptance of the rules of the EU single market and customs union.

Philippe Lamberts, the Belgian MEP, said that the draft text he had seen on Ireland agreed to “full alignment”.

However, even with the nuanced wording there could be serious political ramifications.

While the Democratic Unionist Party has been consulted throughout the process, the fact that the situation in Northern Ireland vis-à-vis the EU might be different in some ways to that of the rest of the UK post Brexit will cause concerns.

In Edinburgh, Nicola Sturgeon responded to the reports that Northern Ireland and the Republic could maintain regulatory alignment by saying there was no good reason that Scotland could not do the same with the EU and "effectively stay in the single market".

The First Minister tweeted: "If one part of UK can retain regulatory alignment with EU and effectively stay in the single market (which is the right solution for Northern Ireland) there is surely no good practical reason why others can't."

As the Prime Minister sat down for lunch with Mr Juncker, Downing Street responded to reports of the draft agreement and the phrase "regulatory alignment," insisting the UK's "territorial and economic integrity will be protected".

Donald Tusk, the European Council President, said the two sides were "getting closer" to making the required "sufficient progress" for him to recommend at next week’s EU summit that negotiations move on to trade and a transition period.

He tweeted: "Tell me why I like Mondays! Encouraged after my phone call with Taoiseach @campaignforleo on progress on #Brexit issue of Ireland. Getting closer to sufficient progress at December #EUCO."

As the Cabinet of the Irish Government met, Simon Coveney, the Deputy Prime Minister, was upbeat.

“The indications we have is that we are in a much better place now than we have been in the negotiations to date. The legitimate concerns that Ireland has been raising for months are going to be addressed fully.

“These discussions are moving in the right direction. I hope we are in a place this evening where Irish people north and south will get reassurance from the wording that is very close to being finalised now."

Mr Coveney told RTE Radio One that he believed that the post-Brexit border would be "invisible" with "no barriers" and would “look very much like it looks today".

Earlier, David Davis, the Brexit Secretary, appeared relaxed, saying: "We have put seven months of work, both sides, into getting to this point and we are hoping that Mr Juncker today will give us sufficient progress so we can move on to trade talks.

"The decision, of course, won't be taken until December 15 but that's what we are hoping for. Because trade talks are of enormous importance to the United Kingdom and to Europe.”

Acknowledging that today was the day set by Mr Tusk for Britain to make more concessions so sufficient progress could be deemed to have been made, Mr Davis stressed: "It's an important day. Everybody understands that the decision to move on to trade talks is vital."

While not all details have been agreed on the three key phase one issues, progress has been made; the key is whether or not it is deemed by the EU27 to be sufficient.

On the divorce bill, the Government has moved to accepting that the EU27 should not lose out by the UK’s departure and, while a precise figure has not been accepted, the ball-park of 50 billion euros over several years seems to be the target to which both sides are now moving.

On citizens’ rights, the Government has moved to reassure those living in the UK that the process of registering and remaining will be straightforward; however, the key sticking point of any role beyond Brexit for the European Court remains unresolved.

On the Irish border, Dublin, which was handed a veto by Brussels on progressing the talks to phase two, seems to have been reassured and persuaded to accept a form of words that will remove this barrier; yet just how an open border will operate practically post Brexit still needs resolving.

Minutes before sitting down for lunch with Mrs May, Mr Juncker held talks with Leo Varadkar, the Taoiseach, as reports were being aired of a major compromise on the border.

Following her lunch, the PM will hold talks with Mr Tusk, who is organising next week’s EU summit, when any breakthrough to take the talks to the second phase on trade and transition will be formally ratified.

A joint UK-EU statement is expected later today.