In a joint statement released after more than two hours of intense talks, the pair admitted “challenges” remained over how to avoid customs checks at the border between Northern Ireland and the Irish Republic but agreed to “reflect” on the way forward. And Mr Varadkar insisted that, while differences over the Irish border row still needed to be resolved, he thought a “treaty” could be signed in time to allow the UK to quit the EU on October 31. The statement said: “The Prime Minister and [Irish premier] have had a detailed and constructive discussion.
“Both continue to believe that a deal is in everybody’s interest. They agreed that they could see a pathway to a possible deal.
“Their discussion concentrated on the challenges of customs and consent.
“They also discussed the potential to strengthen bilateral relations, including on Northern Ireland.
“They agreed to reflect further on their discussions and that officials would continue to engage intensively on them.”
The statement said Mr Vardakar would brief the EU’s negotiating team on their discussions while Brexit Secretary Stephen Barclay will meet Brussels diplomat Michel Barnier this morning.
Mr Varadkar struck an even more positive note when speaking to broadcasters after the meeting.
He said: “What I can say is 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 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.”
Mr Varadkar doubted whether a deal could be finalised in time for next week’s EU summit but thought it possible to conclude the agreement in time for Mr Johnson’s Halloween deadline.
He added: “It remains our position that there can’t be a hard border between north and south.”
Irish government sources suggested the meeting would help to renew the negotiations.
Cabinet Office Minister Michael Gove, who is in charge of the U.K.’s no-deal preparations, said: “I think it is very encouraging again I know that the Prime Minister and Taoiseach spoke privately for quite some time before bringing in their officials. I know the tone was positive from that meeting.
“And I know the Irish government will be briefing Michel Barnier and the taskforce 50 team.
“So I hope the optimistic and constructive approach that both sides showed can result in more progress and I am looking forward to talking to the Prime Minister tomorrow about what more progress we might be able to make.”
He added: “I have to prepare for every eventuality but I’m hopeful following the good conversation that they had that we can make good progress in the days ahead.”
Yesterday’s talks between the Prime Minister and his Irish counterpart were held at the 19th century Thornton Manor, usually a wedding venue.
It followed a furious clash between Mr Johnson and German Chancellor Angela Merkel earlier this week that left the negotiations on the brink of collapse ahead of a crunch EU Council summit in Brussels next week.
She made clear the EU would not accept a Brexit deal that allowed Northern Ireland to leave the bloc’s customs union, claiming such an outcome would put the province’s peace process at risk by raising the threat of the return of checks at the Irish border.
The meeting followed a hint from Business Secretary Andrea Leadsom that the Prime Minister was gearing up to by-pass legal obstacles to a no-deal Brexit by sending one letter requesting an extension and, in the same instance, submitting a second memo telling European leaders he does not.
The Benn Act demands the PM request a delay to the Article 50 deadline until January 2020 if a deal has not been agreed before October 19.
Mr Johnson has repeatedly said that while he will abide by the law, he will be taking the UK out of the EU on October 31, with or without a deal.
Asked on ITV’s Peston programme whether the idea of sending two letters to the EU was a possible loophole, Mrs Leadsom replied: “Absolutely.”