(CNBC) Despite parliament defeat, Britain’s May on course to deliver Brexit

Noting that the EU executive delivered its crucial verdict last week of “sufficient progress” on divorce terms to allow the opening of talks on the future, she added: “I’m looking forward to discussing that deep and special partnership for the future.”

A senior British government official said that the prime minister would press for a quick agreement on a transition deal to allow businesses to adapt to life after Brexit.

“The prime minister will say that reaching the agreement on phase one has required give and take on both sides but a fair outcome has been achieved,” the official told reporters.

Acknowledging the tough negotiations ahead, Donald Tusk, chairman of the EU leaders, warned them that only their unity displayed so far in the Brexit talks would deliver a good deal as discussions move to trade — an issue on which the member states have widely divergent interests.

“I have no doubt that the real test of our unity will be the second phase of Brexit talks,” Tusk told reporters.

Phase one covered Britain’s bill to the EU, the border with Ireland and the status of EU citizens in Britain.

After days of often fraught diplomacy, May rescued the initial deal last Friday, easing the concerns of her Northern Irish allies over the wording to protect a free border with EU member Ireland without separating the province from the UK.

Then, EU negotiators said the talks had made “sufficient progress”, a recommendation that will, barring accidents, be blessed by the leaders of the other member states.

German Chancellor Angela Merkel said there was a good chance that the next phase of Brexit negotiations could begin.

“Progress has been made regarding the exit of Great Britain, but there are some open questions so it is good that we will talk about it tomorrow,” she said. In fact, diplomats say there is virtually no doubt that leaders will endorse the decision.

May’s success has won her some respite at home from political in-fighting between enthusiasts and sceptics of Brexit in her ruling party, and has reduced the prospect of a disorderly departure from the bloc.

But there are hurdles still to negotiate. May and her cabinet are due next Tuesday to hold a discussion of senior ministers’ competing views on Britain’s future outside the EU — to remain close to the bloc or forge a new path.

She also faces a newly emboldened parliament after rebels in her own party joined forces with opposition lawmakers to demand that Parliament not the government gets the final say on the deal — a defeat they may try to repeat next week when May puts Britain’s departure date into a bill to sever ties.

But May was quick to point out that the government had won 35 of 36 votes with average majority of 22, refusing to back down and keen to speak up the chances of a good trade deal.

The EU is willing to start talks next month on a roughly two-year transition period to ease Britain out after March 2019 but wants more detail from London on what it wants before it will open trade negotiations from March.

Before dinner on Thursday, May and her EU peers will discuss the bloc’s plan for closer defence cooperation with NATO Secretary-General Jens Stoltenberg. Long blocked by London, the plan now has backing from Britain, which as one of Europe’s main military powers, wants to keep ties with the EU on defense.

Over dinner, leaders will discuss their response to the migration crisis from Africa and the Middle East, and lingering deep divisions over how to share the load.

They will confirm a rollover of sanctions on Russia over the Ukraine crisis and are likely to reaffirm their opposition to U.S. President Donald Trump’s move to recognise Jerusalem as the capital of Israel.