Theresa May has welcomed the European Council's agreement to give the green light for Brexit talks to move on to their second phase, dealing with the transition to a new relationship after the UK's withdrawal.

The momentous step was agreed in a meeting of the leaders of the 27 remaining EU states lasting less than half an hour in Brussels in the Prime Minister's absence.

Guidelines agreed at the European Council summit revealed that the EU expects Britain to remain under the jurisdiction of the European Court of Justice and permit freedom of movement during a transition period expected to last two years after the official date of Brexit in March 2019.

European Council president Donald Tusk announced the decision on Twitter: "EU leaders agree to move on to the second phase of #Brexit talks. Congratulations PM @theresa_may."

And Mrs May responded by thanking Mr Tusk and European Commission president Jean-Claude Juncker, adding: "Today is an important step on the road to delivering a smooth and orderly Brexit and forging our deep and special future partnership."

Mrs May left the two-day summit early after winning applause from the other leaders as she assured them on Thursday evening of her determination to see Brexit through despite this week's defeat in the House of Commons.

The EU position set out in the guidelines makes clear that any transition period agreed by Brussels "must be in the interest of the Union, clearly defined and precisely limited in time".

Under the proposals, the UK will be required to follow the EU rulebook in its entirety - including laws adopted during the transition period - while playing no part in the decision-making processes of the European institutions.

And the guidelines make clear that Britain will be expected to observe the single market's "four freedoms" of movement of goods, services, people and capital during the period, expected to begin on March 29 2019.

During the transition, the guidelines state, "all existing Union regulatory, budgetary, supervisory, judiciary and enforcement instruments and structures will ... apply, including the competence of the Court of Justice of the European Union.

"As the United Kingdom will continue to participate in the Customs Union and the Single Market (with all four freedoms) during the transition, it will have to continue to comply with EU trade policy, to apply EU customs tariff and collect EU customs duties, and to ensure all EU checks are being performed on the border vis-a-vis other third countries."

The four-page guidelines pour cold water on Brexiteers' hopes of a swift movement to detailed negotiations on a free trade agreement with the EU.

They confirm that agreement on a future trade relationship can only be finalised once the UK has formally left the EU.

And they state that the EU is currently ready only to engage in "preliminary and preparatory discussions with the aim of identifying an overall understanding of the framework for the future relationship" after additional guidelines have been adopted at a future summit in March.

In a key passage hinting at the obstacles which lie ahead of a trade deal, the document notes that the UK has expressed its desire to leave the single market and customs union, and that the EU will therefore have to "calibrate" its approach on trade and economic co-operation to "ensure a balance of rights and obligations, preserve a level playing field, avoid upsetting existing relations with other third countries, and ... preserve the integrity and proper functioning of the Single Market".

The European Council confirmed its readiness to maintain co-operation with the post-Brexit UK in the fight against terrorism and international crime, as well as security, defence and foreign policy.

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Mrs May said: "We will deliver on the will of the British people and get the best Brexit deal for our country - securing the greatest possible access to European markets, boosting free trade with countries across the world, and delivering control over our borders, laws and money."

In a sign of the consternation sparked in Brussels by David Davis's suggestion that last week's divorce deal amounted to no more than a "statement of intent", the EU27 warned that "negotiations in the second phase can only progress as long as all commitments undertaken during the first phase are respected in full and translated faithfully into legal terms as quickly as possible".

The leaders of the remaining 27 member states agreed that last Friday's deal between Mrs May and European Commission President Jean-Claude Juncker amounted to "sufficient progress" to move negotiations on to their second phase.

That deal, covering the divorce issues of citizens' rights, the Irish border and the UK's £39 billion exit bill, will now be transformed into a legally binding form to be signed by October ahead of ratification by the European Parliament, Westminster and national assemblies around the EU.

Friday's decision was considered little more than a formality after Mr Juncker and chief Brexit negotiator Michel Barnier said they believed "sufficient progress" had been made, and the European Parliament overwhelmingly endorsed that verdict in a vote on Wednesday.

Danish Prime Minister Lars Lokke Rasmussen welcomed the development, saying: "Now ready to move to phase two. Hope for close future relations with UK after Brexit."

EU leaders were putting pressure on Mrs May to spell out precisely what the UK wants on trade, with Maltese Prime Minister Joseph Muscat saying: "I think the first really big step is for the UK to say pretty clearly what it wants, in clear terms.

"I think that if this happens within the next few weeks, we can start in earnest and by March we will have a very clear European position."

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In a move likely to be welcomed in London, the EU27 said new negotiating directives on transitional arrangements could be adopted as early as January 2018.

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