Theresa May and the EU have announced that a breakthrough deal has finally been reached to move the Brexit talks onto future trade and a transitional period, after days of tortuous negotiations.

The Prime Minister arrived in Brussels before 6am on Friday, to stage a joint press conference with EU leaders – following discussions with the Democratic Unionist Party that stretched long into the night.

Standing alongside Ms May, Jean-Claude Juncker, the European Commission President, said “sufficient progress” had been made on all three so-called “divorce issues” – the Irish border, a financial settlement and EU citizens’ rights.

Ms May said it “hasn’t been easy for either side”, árguing there had been “give and take on both sides” to strike an agreement that was a “significant improvement”.

And she pointed to the prize of successfully moving onto talks on future trade, saying: “Doing so will provide clarity and certainty for businesses in the United Kingdom and the European Union.”

The Prime Minister also argued she had reached a financial settlement “fair for the British taxpayer”. It is expected to be at least £45bn – with top-up payments for future market access likely.

But Ms May claimed the payout would allow the Government to “invest more in our priorities of housing, schools and the NHS”.

And, on the Irish border, she admitted that “specific solutions to what are the unique circumstances of Northern Ireland” would still need to be found – suggesting the deal was still a fudge.

On EU citizens, Mr Juncker pointed to possible trouble ahead, saying: “For EU citizens, the ECJ [European Court of Justice] will still be competent.”

The text of the agreement showed disputes involving EU citizens in the UK can be referred to the ECJ for eight years - longer then the UK wanted and a likely flashpoint with hard Brexit-supporting Tory MPs.

Moments later, Donald Tusk, the EU Council President, representing the member states, said the UK – in a transition period – would have to accept the “whole of EU law – including new law”.

Brexit bonhomie as May finally seals agreement with EU leaders Show all 10 1 /10 Brexit bonhomie as May finally seals agreement with EU leaders Brexit bonhomie as May finally seals agreement with EU leaders Britain's Prime Minister Theresa May is welcomed by European Commission President Jean-Claude Juncker Reuters Brexit bonhomie as May finally seals agreement with EU leaders EU President Jean-Claude Juncker greeting Theresa May at the EU Commission in Brussels PA Brexit bonhomie as May finally seals agreement with EU leaders Britain's Prime Minister Theresa May poses for a picture with European Council President Donald Tusk REUTERS Brexit bonhomie as May finally seals agreement with EU leaders EU Commission President Jean-Claude Juncker walks behind British Prime Minister Theresa May EPA Brexit bonhomie as May finally seals agreement with EU leaders British Prime Minister Theresa May (L) and European Commission President Jean-Claude Juncker address a press conference at the European Commission in Brussels AFP/Getty Images Brexit bonhomie as May finally seals agreement with EU leaders British Prime Minister Theresa May speaks at a press conference with EU Commission President Jean-Claude Juncker EPA Brexit bonhomie as May finally seals agreement with EU leaders Britain's Secretary of State for Exiting the European Union, David Davis (L) and Michel Barnier (2-L), the European Chief Negotiator of the Task Force for the Preparation and Conduct of the Negotiations with the United Kingdom under Article 50 enter the room by the emergency exit to attend British Prime Minister Theresa May press briefing on Brexit Negotiations in Brussels. EPA Brexit bonhomie as May finally seals agreement with EU leaders Britain's Secretary of State for Exiting the European Union David Davis (L), Britain's Prime Minister Theresa May (2-L), European Commission President Jean-Claude Juncker (2-R) and European Union's chief Brexit negotiator Michel Barnier (R) in a meeting on Friday morning AFP/Getty Images Brexit bonhomie as May finally seals agreement with EU leaders European Union chief Brexit negotiator Michel Barnier speaks during a media conference at EU headquarters Brexit bonhomie as May finally seals agreement with EU leaders European Council President Donald Tusk addresses a media conference at the Europa building in Brussels AP

In Belfast, Arlene Foster, the DUP leader, said she had secured “six substantive changes” to the text which it vetoed on Monday over the issue of “regulatory alignment” with the EU, to avoid a hard land border in Ireland.

The DUP had stamped on the proposal, ruling out anything that treated Northern Ireland differently from the rest of the UK – and claimed it had won concessions.

“There is no red line down the Irish sea and clear confirmation that the entirety of the UK is leaving the European Union, leaving the single market and leaving the customs union,” Ms Foster said.

But she warned: “There are still matters there that we would have liked to see clarified. We ran out of time, essentially. We think we needed to go back again and talk about those matters, but the Prime Minister has decided to go to Brussels.” Ms Foster suggested the DUP could still vote against the final Brexit deal.

The agreement gives the Stormont Assembly - when restored - a block on any new trade barriers between the Northern Ireland and the UK, in the absence of an over-arching free trade agreement with the EU after March 2019.

The crucial text reads: “In the absence of agreed solutions, the United Kingdom will maintain full alignment with those rules of the Internal Market and the Customs Union which, now or in the future, support North-South cooperation, the allisland economy and the protection of the 1998 Agreement.”

The Irish Government insisted it had achieved all that it had been seeking in the intensive negotiations over the last few days, pointing to a “guarantee of avoiding a hard border”.

Mr Juncker stressed that the deal remained a Commission recommendation, saying: "The decision on sufficient progress will be in the hands of the 27 heads of state or government.” They meet at a summit next Thursday.

Ms May was asked whether she had ever considered during negotiations that “maybe after all, this whole Brexit affair is a very bad idea”. She replied: “The British people voted and they voted to leave the European Union.

“I believe it's a matter of trust and integrity in politicians. I believe the people should be able to trust that their politicians will put into place what they have determined. That's exactly what we are doing and we will leave the European Union.”