British Prime Minister Theresa May arrives in Brussels on Thursday for the first day of a European Union summit. Leaders are to vote Friday on moving to the second stage of Brexit negotiations. (John Thys/AFP/Getty Images)

European leaders were ready Thursday to give a green light to a crucial new stage of Britain's negotiations to leave the European Union, as fresh divisions in London highlighted the challenge Prime Minister Theresa May faces selling any deal to her country.

A humiliating parliamentary vote on the eve of the E.U. summit underlined May's weakness as she prepared for initial trade talks with the bloc. Pro-E.U. members of May's Conservative Party joined forces with the opposition Wednesday to override their leader's wishes by giving lawmakers a vote on the final Brexit deal.

The move followed an interim agreement, announced last week, in which May capitulated on the European Union's key demands about how much money Britain will owe as it leaves, the rights of the 3 million E.U. citizens in Britain, and the bloc's desire for an open border between Ireland and Northern Ireland.

[Britain and E.U. reach divorce deal to move on to new phase in Brexit talks]

The commitments were so wide-ranging that British negotiators struggled to explain how they would hold to them and also deliver on May's vows to ultimately have a full split from the E.U.

As May entered the meeting with E.U. ministers on a drizzly Brussels afternoon, she sought to put a brave face on the parliamentary vote, which she lost 309 to 305.

"I'm disappointed," she said of the lawmakers' rebellion, but added: "We're on course to deliver Brexit. We're on course to deliver on the vote of the British people."

European leaders have threatened that if Britain's Parliament rejects the Brexit deal agreed to last week by the May government, the E.U. will not be in a mood to renegotiate. Brussels officials were unsettled by comments last weekend by Brexit Secretary David Davis, who said the deal was only "a statement of intent" rather than something binding.

Still, most heads of state indicated Thursday that they planned to approve moving on to the next stage in the second day of meetings Friday.

Davis's dismissive remarks made clear that resolution of many thorny issues has been postponed rather than finalized.

Such statements cause concern, said Dutch Prime Minister Mark Rutte.

"An eyebrow was raised here and there because of that comment," Rutte said as he entered the summit locale. "But I think it makes it more necessary to have as soon as possible that deal of last Friday in legally binding text, so that we cannot have a misunderstanding on what was exactly agreed."

European leaders plan to find a way to "David Davis-proof" the agreement, said a senior E.U. official who spoke on the condition of anonymity under ground rules to brief reporters before the summit.

"The joint report is a binding document, not an exercise in sleight of hand to enable us to move on to the second phase," European Parliament President Antonio Tajani told lawmakers Thursday.

There was also a flurry of worry over whether May's government would stick to its promise to keep open the border between the Republic of Ireland and Northern Ireland, which might require Britain to adopt rules and regulations nearly identical to those in force now.

Irish leaders have made clear that an open border is a red line for them, and they have been backed by the 26 other remaining E.U. nations.

Leo Varadkar, the Irish prime minister, told Sky News, "I have absolute confidence and trust in the prime minister and the British government that they will stand by the political agreement that was made last week."

[This is why Irish politicians are frustrated with the U.K.’s Brexit negotiations]

But it remained unclear whether the full implication of May's commitment had filtered into Britain's political consciousness. The prime minister has separately promised that there will be no special E.U. regime for Northern Ireland that could create a split with the British mainland — and that Britain will enjoy expansive new opportunities to forge an independent trade policy with the rest of the world.

The commitments do not appear to fully add up, given that an open border with Ireland would force British regulations and policies to be closely aligned with those of the European Union. European diplomats involved in the negotiations said ahead of this week's summit that they saw some contradictions, but they said that was May's domestic political problem to solve, not theirs.

"You could imagine a situation in which the rules are more or less identical after Britain leaves," said Fabian Zuleeg, the head of the European Policy Center, a Brussels-based think tank. But, he said, "the whole purpose of Brexit was to have policy divergence."

No matter how the Irish issue is resolved, Britain's freedom to follow a path independent of Europe seems likely to be postponed, with trade talks between the two sides stretching on for years. For now, Britain increasingly appears headed for a state of limbo after its formal exit, in which it will be subject to E.U. rules and payment obligations without having a role in decision-making as the trade deal is worked out.

Some E.U. leaders already are worried that the unusual degree of unity among the remaining 27 member countries in the first stage of talks with Britain will fall apart in the trade discussions, given nations' competing interests. It is likely that disagreements would only impede a deal rather than improve London's bargaining power, because European countries each hold a veto on the overall bargain.

"The real test of our unity will be the second phase of Brexit talks," the European Council's president, Donald Tusk, said Thursday.

Booth reported from London. Karla Adam in London contributed to this report.

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