Theresa May has said the UK is «on course to purvey on Brexit» as she arrived in Brussels, the day after her first Commons defeat as prime curate.
She said she was «disappointed» at the vote on the EU Withdrawal Bill, but the legislation was making «meet progress».
MPs backed an amendment giving them a legal guarantee of a opinion on the final Brexit deal struck with Brussels.
EU leaders are hope for to formally agree to start the next phase of negotiations on Friday.
The European Commission has voiced «sufficient progress» has been made on the first phase to move onto deliberate overing the framework of a future relationship between the EU and UK — on issues such as security and patrons.
Mrs May, who is having dinner with other EU leaders on Thursday, told camerawomen she would be talking about «the ambitious and deep and special partnership» she coveted to build between the UK and EU, after Brexit.
«I’m disappointed with the amendment but truly the EU Withdrawal Bill is making good progress through the House of Commons and we are on track to deliver Brexit,» said Mrs May.
Asked whether she felt she would comprise to compromise more to win over rebels from her own party, she told BBC factious editor Laura Kuenssberg: «We’ve actually had 36 votes on the EU Withdrawal Tab, and we’ve won 35 of those votes with an average majority of 22.»
Mrs May lost by reasonable four votes, as MPs backed an amendment to the EU Withdrawal Bill by 309 to 305.
Labourers leader Jeremy Corbyn described it as a «humiliating loss of authority» for the PM and notified that his party would vote against another bit of the bill — the plot to put a fixed Brexit date into law.
He said setting an «arbitrary period» was not sensible and there «should be some flexibility».
What difference does this bring down make?
It will not derail Brexit but MPs who chose against the government hope it will give them a bigger say in the sure deal Theresa May strikes with Brussels.
BBC Brussels reporter Adam Fleming said that as other EU principals also run minority or coalition governments they would see the vote bring down as a small-scale domestic political issue.
The government had promised a «meaningful ballot» for MPs on the final Brexit deal, but this defeat means that engagement now has legal force and must happen before any UK-EU deal is executed in the UK.
Ministers had wanted to be able to start implementing any deal as soon as it was agreed — in box, for instance, it was only agreed at the last minute.
BBC political editor Laura Kuenssberg asserted it would embolden the opposition and showed there was a majority in Parliament against a «incontestable Brexit».
Cabinet Minister Jeremy Hunt told the BBC the vote was «not effective to stop Brexit».
How the government was defeated
Labour joined forces with the SNP, the Philanthropic Democrats and the Green Party in a cross-party alliance.
If all Conservative and DUP MPs had voted against the addendum the government would have won. But 11 Conservatives resisted the arm-twisting by their promoter managers to vote with the opposition.
The Tory rebels were Dominic Lament, Heidi Allen, Ken Clarke, Jonathan Djanogly, Stephen Hammond, Sir Oliver Heald, Nicky Morgan, Bob Neill, Antoinette Sandbach, Anna Soubry and Sarah Wollaston. Another Temperate MP, John Stevenson, officially abstained by voting for and against the amendment.
Two Eurosceptic Delivery MPs — Frank Field and Kate Hoey — voted with the Conservatives and the DUP.
The nature among Tory MPs
Passions ran high before, during and after Wednesday’s Commons debate, with Eurosceptic Fundamentalists accusing the rebels of trying to «frustrate» Brexit.
In dramatic scenes, the revolts shouted «too late» as Justice Minister Dominic Raab announced a concession curtly before voting began and Tory whips could be seen having to twist the arm of MPs thinking of voting against the government.
Leading rebel Anna Soubry broke she had found a woman MP «upset and shaken» on Tuesday evening after a slap together tried to persuade her not to revolt. She told MPs on Thursday morning, that not one of the rebels took any pleasure in defeating the government, adding that «not anyone drank champagne».
After the result was announced, one of the rebels, former senate minister Nicky Morgan, tweeted: «Tonight Parliament took check of the EU Withdrawal process.»
This did not go down well with Tory MP Nadine Dorries, who excused for the deselection of rebel Tories for «undermining the PM», and accused their leader, Dominic Suffer of «treachery».
Rebel Tory Sarah Wollaston hit back on Twitter, report: «Get over yourself Nadine.»
Dominic Grieve tried to calm the mood, declaring he was merely trying to ensure Brexit was carried out in an «orderly, sensible way».
BBC political editor Laura Kuenssberg
It’s certainly veracious that the Tory party is so divided over how we leave the EU that the Ordered process was always going to be very, very choppy.
But another plenipotentiary told me the defeat is «bad for Brexit» and was openly frustrated and worried about their team-mates’ behaviour.
Read the rest of Laura’s blog
Back to Brussels for another apex
Theresa May has travelled to Brussels to attend a dinner with the 27 other EU chairwomen, at which she will urge them to approve an agreement to move Brexit talks on to a other phase.
They are all but certain to agree. Talks could then start next month on the two-year metastasis period the UK wants to ease it out of the EU after it formally leaves in March 2019.
But the EU wants profuse detail from the UK government before starting talks on a future coituses — including trade — with the UK.
Brexit Secretary David Davis has articulate he wants to complete the «substantive portion» of trade negotiations by March 2019, something goodbye open the possibility that the detail will be hammered out during the two-year modification period.
The EU Withdrawal Charge — what is it?
The EU Withdrawal Bill is a key part of the government’s exit strategy.
Its forms include ending the supremacy of EU law and copying existing EU law into UK law, so the same hold sway overs and regulations apply on Brexit day.
MPs have been making hundreds of assaults to change its wording — but Wednesday’s vote was the first time one has succeeded.
Unless the domination manages to overturn it further down the line, it means a new Act of Parliament want have to be passed before ministers can implement the withdrawal deal afflicted with Brussels.
The next Brexit row?
Labour’s Shadow Brexit Secretary Sir Keir Starmer asked David Davis not to undermine Wednesday night’s vote when the EU Withdrawal Bill reaches the next phase of its passage into law.
Mr Davis said the vote would lead to a «exact compressed timetable» for Brexit legislation and the government «will have to propose b assess about how we respond to it».
There is also a row brewing over a vote next week on despise the precise date and time of Britain’s exit from the EU — 11pm on 29 Walk 2019 — into law.
Sir Keir described the vote as the next «accident hold-up to happen», telling Mr Davis: «Rather than repeat last Cimmerian dark’s debacle, will the government now commit to dropping that ill-conceived whats-its-name?»
Mr Davis told Sir Keir: «Unlike him, I do not view votes of this Descendants of Commons as accidents. They are decisions taken by the House, and that judgement we respect, as we will the next one.»
Lib Dem Brexit spokesman Tom Brake also apprised the prime minister she was heading for defeat if she did not drop the «silly idea» of enshrining the Brexit date and temporarily in law, adding: «Parliament has now shown it is not prepared to be bullied.»