'Significant progress' in Theresa May's talks with the DUP

"Discussions are going well with the government and we hope soon to be able to bring this work to a successful conclusion", the DUP's Arlene Foster said after the meeting.

The talks with the DUP follow May's apology to Conservative rank-and-file lawmakers in a meeting Monday which signaled she would be more open to consultation, particularly with business leaders demanding answers about the details on Britain's departure from the European Union.

While the DUP are deeply Eurosceptic, they have balked at some of the practical implications of a so-called hard Brexit - including a potential loss of a "frictionless border" with the Republic of Ireland - and talks will touch on efforts to minimise the potential damage to Northern Ireland.

May needs all the help she can get, given the near-impossibility of the challenge she now faces.

Labour leader Jeremy Corbyn turned Mrs May's election slogans against her, claiming a link-up between the Tories and DUP would be a "coalition of chaos".

The first test of any deal is expected to come at the Queen's Speech - a formal occasion at which the government asks parliament to approve its legislative agenda.

The deal has also caused consternation in Dublin, with Irish premier Enda Kenny warning such an alliance could upset Northern Ireland's fragile peace. "I think it's much more likely that the party will be looking for money in order to benefit Northern Ireland".

He told BBC Radio 4's World at One programme: "The last thing anybody wishes to see is one or other of the communities so aggrieved that the hardmen, who are still there lurking in the corners of the communities, decide that they wish to return to some form of violence". Labour may have won 30 seats, but it still falls 64 seats short of a possibility to form a majority government, and even if it aligned with all other left-leaning parties such as the Liberal Democrats of the Greens, that would still not be almost enough to challenge the Conservatives.

"The people of Britain have had a bellyful of promises and politicking. There's a lot of anxiety", Sinn Fein MP Michelle Gildernew told AFP.

The UK Government undertook in the Belfast Agreement in 1998 to be impartial in Northern Irish politics.

"So we should set up a small cross-party commission to conduct the negotiations, and have a clear and transparent process to build consensus behind the final deal".

But a lacklustre campaign saw her high approval rating slip away, and support for her "hard Brexit" strategy - pulling out of the European single market and customs union - now hangs in the balance.

"I am concerned [by the need] to have a partner for the negotiation as quickly as possible", Barnier said.

"My preoccupation is that time is passing, it is passing quicker than anyone believes because the subjects we have to deal with are extraordinarily complex", he added.

"We have seen in Northern Ireland over very many years that events always don't unwind as you expect them to unwind", he said.

Michel Barnier urged Mrs May to "very quickly" start talks and appoint a negotiating team that is "stable, accountable and with a mandate" with the clock ticking to March 29 2019, when the United Kingdom is expected to leave after the two-year Article 50 process. Thus we must begin this negotiation.

Mr Barnier, a former minister in the French government, said Britons had the right to know the "consequences" of leaving the EU.

The EU meanwhile was preparing to unveil plans to give itself new powers over London's banking business after Brexit in a blow to the city's supremacy as a global financial hub.

But since coming to power three weeks after the shock vote to leave the European Union, the prime minister has advocated a hard Brexit, which would entail Britain leaving the single market and cutting immigration from the bloc.

Mrs May said nothing to reporters as she left Downing Street by auto shortly after 2.15pm for a trip to France to meet the new French president.