Taoiseach Leo Varadkar has said he and Boris Johnson have found a pathway that could allow Britain to leave the European Union with a deal by the end of this month.

He was hopeful that their three hours of discussions at Thornton Manor hotel outside Liverpool had produced the basis for formal negotiations to resume in Brussels.

“I think sometimes at this point in negotiations and discussions, the less said the better. But what I can say is that I had a very good meeting today with the prime minister and our teams together - very positive and very promising. I am now absolutely convinced that both Ireland and Britain want there to be an agreement,” he said.

"That's in the interests of Ireland [and] the United Kingdom and the European Union as a whole. And I do see a pathway towards an agreement in the coming weeks."

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The venue was kept secret until just before the two leaders arrived for their lunchtime meeting, which was closed to the media. For most of their discussions, the two leaders were alone, but they were joined by officials, including Mr Johnson’s senior adviser Dominic Cummings, at different times during the meeting.

In a joint statement after the meeting, the Taoiseach and the prime minister said it had been “a detailed and constructive” discussion that had dealt with the two most difficult outstanding issues –customs and the role of the Stormont institutions. The Taoiseach said it was not appropriate to talk about concessions made by one side or the other.

“I don’t think this should be seen in the context of who’s making concessions or who the winners and losers are. I don’t think that’s the game any of us want to play. What this is about is securing an agreement that works for the people of Ireland and also the people of Britain and Europe,” he said.

The Taoiseach said he believed Ireland's objectives could be achieved and he declined to state that Northern Ireland must remain part of the EU customs union after Brexit. Mr Johnson insists that Northern Ireland must leave the customs union with the rest of the UK.

“It remains our position that there cannot be a hard Border between North and South. And we must continue to have a situation whereby the all-island economy can continue to deepen and function well,” Mr Varadkar said.

All-Ireland regulatory zone

Mr Johnson’s plan envisages an all-Ireland regulatory zone for all goods, so that Northern Ireland will effectively remain in the European single market. But he wants those arrangements to be subject to the consent of the Northern Ireland Executive and Assembly, which would have to approve them in advance and renew that endorsement every four years.

Irish officials debriefed the EU's Brexit taskforce after the meeting and EU chief negotiator Michel Barnier will meet Brexit secretary Stephen Barclay on Friday to determine if there is a basis for a resumption of formal negotiations.

“I think it is possible for us to come to an agreement, to have a treaty agreed to allow the UK to leave the EU in an orderly fashion, and to have that done by the end of October. But there’s many a slip between cup and lip,” Mr Varadkar said.

The advance notice of the meeting, the wording of which was agreed between Government Buildings and Downing Street, said only that the talks would be “about the process for securing agreement for a Brexit deal” and not, Irish sources pointed out, about actually securing an agreement on the substance on how the UK leaves the EU.

Dublin has repeatedly refused to negotiate directly with the UK on Brexit, insisting that the negotiations can only take place between the British government and the EU taskforce under Mr Barnier.

On Wednesday, Mr Barnier said it was not currently possible to reach agreement with the UK, and there was little expectation in Brussels that any breakthrough is possible to enable EU leaders to approve a deal at next week’s summit.

Northern Ireland

On Wednesday in the Dáil, Mr Varadkar stressed the views of the people of Northern Ireland, who voted to remain in the EU.

“Part of the difficulty at the moment is that it is the position of the UK government that Northern Ireland must leave the EU customs union and be part of the UK customs union no matter what the people of Northern Ireland think,” he said. “That is its position and that creates a grave difficulty for us because we want there to be a deal that respects the wishes of the people of Northern Ireland and the people in this Republic too.”

Officials said Dublin was open to discussing how mechanisms could work to attain the consent of the Northern Ireland institutions, but remained opposed to any veto for the DUP.

The meeting on Thursday was the second meeting between the two leaders in the space of three weeks. They also spoke by telephone earlier this week.

Tánaiste Simon Coveney said there was cause for optimism after the talks but that there was still some way to go before they had got an agreement.

“Mark my words we are not there yet,” Mr Coveney said in a speech in Dublin before meeting Mr Varadkar on his return from the talks.

Fianna Fáil leader Micheál Martin welcomed Thursday’s developments, tweeting: “I’m pleased that the megaphone diplomacy has been replaced by proper & serious #Brexit discussion today.”

‘Super Saturday’

Also on Thursday, reports emerged that Pro-Remain MPs are planning a crunch vote on a second referendum on Brexit during the “super Saturday” sitting of parliament.

Several MPs involved in the People’s Vote campaign said the special parliamentary session on October 19th could be the key moment when the House of Commons will test whether there is support for a second referendum.

Elsewhere in Britain, de facto deputy prime minister Michael Gove claimed the Scottish government has undermined the Brexit process so that it can “smash up the United Kingdom”.

The comments come after Scottish Brexit secretary Mike Russell said the relationship between Westminster and the devolved administrations has deteriorated. Additional reporting: Reuters/PA/Guardian