The Latest on the Brexit talks (all times local):
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British Prime Minister Theresa May has told leaders of the European Union's 27 other member states at a summit that she is committed "to delivering a smooth and orderly exit from the European Union."
A senior British government official told reporters that May told them over dinner Thursday that she wants to move onto the next phase of negotiations "with ambition and creativity."
Britain and the EU finally made a breakthrough after months of negotiation on their divorce deal, with the European Commission saying that enough progress had been made on three key issues to move the talks to the next phase.
The official, who spoke on condition of anonymity, said that a priority is to bring greater certainty to business in the UK and across the other 27 member states.
The official quoted May as saying that "while many will say that the last few months show how difficult these future negotiations will be, the UK and the EU have demonstrated what can be achieved with commitment and perseverance on both sides."
A British official says Prime Minister Theresa May wants the United Kingdom to remain part of the Erasmus student exchange program at least through to the end of 2020 — almost two years beyond the scheduled date of Brexit.
The 30-year-old program is one of the bloc's most popular achievements and has allowed millions of young Europeans to study in other countries by funding their studies. The program includes several non-EU states, including Iceland and Norway.
A senior British official, who briefed reporters at summit of European Union leaders, said May is informing her counterparts from the 27 other EU member states of her aspiration.
He said May told other leaders that she welcomed the chance "to provide clarity to young people and the education sector and reaffirm our commitment to the deep and special relationship we want to build with the EU."
Britain is scheduled to leave the EU on March 29, 2019.
British Foreign Secretary Boris Johnson says the government's House of Commons defeat on a key piece of Brexit legislation will not halt the "unstoppable" Brexit process.
On Wednesday, 11 Conservative lawmakers joined with the opposition to pass a motion giving Parliament the final say over Britain's eventual exit deal with the European Union.
Johnson downplayed the significance of the vote, saying "of course it's right that Parliament should have a vote on the final deal. That was always going to be the case. I don't think that last night's vote really changes those facts."
Speaking at a news conference of U.K. and Japanese foreign and defense ministers, Johnson said "I think Brexit is unstoppable."
Johnson said he did not believe Parliament would "actually vote to stop or reverse the Brexit process or frustrate the will of the British people."
British Prime Minister Theresa May says she is "disappointed" by a vote that gives parliament the final say on any Brexit deal with the European Union.
However, she insisted that plans to exit the bloc are making "good progress" in the House of Commons.
On arriving for a summit of EU leaders in Brussels, May said she was convinced she could still get the bill on Britain's withdrawal from the EU through parliament, and noted that 35 of 36 Brexit-related bills have already been passed.
May said "we are on course to deliver Brexit."
May, whose Conservatives lost their majority in a general election in June, faces more hurdles getting legislation through parliament.
On Wednesday evening, 11 of her party's lawmakers joined up with the vast bulk of the opposition to inflict a loss on the prime minister.
Though the implications of the vote on the type of Brexit that will emerge are unclear, it does mean she will have to give lawmakers a vote on the final Brexit deal that is struck with the EU.
Luxembourg's prime minister, Xavier Bettel, says that Theresa May's defeat in parliament late Wednesday to give the legislature a final say on any exit agreement will make her negotiating stance even more complicated.
He said: "As soon as she negotiates something you will need to go back to London to get an approval from the parliament and this is not making her life easier. It just makes it more complicated for the U.K. government."
May is already hampered by leading a government that needs approval from the DUP party in Northern Ireland.
European Council President Donald Tusk says that the toughest test of unity among the 27 EU nations facing Britain in the Brexit negotiations is still to come.
Both sides agreed last week on what the EU considers sufficient progress on Britain's exit terms: the bill Britain will have to pay the EU, a commitment to keep the border between the EU's Ireland and the U.K.'s Northern Ireland transparent, and the rights of citizens' in each other's territories.
The EU leaders are this week set to give the go-ahead for talks to start addressing a future trade relationship, which will be fraught with divisive and complicated issues.
Tusk said Thursday: "I have no doubts that the real test of our unity will be the second phase of the Brexit talks."
The head of Britain's main business lobby says it is critical for European Union citizens living in the U.K. to gain assurances that their situations will not be changed by Britain's departure from the European Union.
Britain and the other EU states reached a preliminary deal on the status of citizens' in each other's territories, but some doubts were raised when British officials said the deal was only a statement of intent.
Paul Drechsler, the head of the CBI, told The Associated Press that such comments were profoundly unhelpful — particularly because people are staking their lives on the outcome.
Dreschler says "what's the message to EU citizens ... You might be all right, but we can't tell you for another 12 months."
He added "the ambiguity is one thing. But ambiguity about children and their parents and their grandparents is not consistent with British values. The way we are treating people is unacceptable"
Britain's chief Brexit negotiator says a situation in which the U.K. crashes out of the European Union without a deal has become "massively less probable" because of a preliminary agreement reached last week.
Brexit Secretary David Davis told lawmakers on Thursday that a "no-deal" Brexit was now extremely unlikely, although "we continue to prepare for all outcomes."
EU leaders meeting in Brussels Thursday and Friday are expected to sign off on last week's agreement between Britain and the bloc, and to let talks move on to future relations and trade.
The British government is hailing progress in Brussels, but faces trouble at home over Brexit. Late on Wednesday, lawmakers won a House of Commons vote giving Parliament the final say on any deal with the EU.