Theresa May has pressed the EU for a "bespoke" Brexit deal that would allow the UK to control migration while still keeping strong trade links, a spokeman has said.
The prime minister vowed to carry out talks in a "positive and constructive spirit" in a one-on-one meeting with European Commission president Jean-Claude Juncker in Brussels.
It came after she was sidelined at a summit which saw her only allowed to address fellow leaders briefly on the UK's plans for Brexit.
A No 10 spokesman said Mrs May had stressed that Britain would remain a strong partner to Europe even after leaving the bloc, as she tries to set a positive tone on the difficult talks.
The Prime Minister set out that the UK would be looking for a bespoke model rather than an 'off the shelf' solution.
She explained that we would needto see controls on the numbers of people who come to Britain from Europeas well as a positive outcome for those who wish to trade in goodsand services.
They agreed we should approach the Brexit negotiations in a positive and constructive spirit to ensure the process is as smooth and orderly as possible.
Talks aimed at establishing a free trade deal between Canada and the EU are reported to have failed.
Canada's trade minister Chrystia Freeland announced the intense talks had broken down as she walked out of meetings with EU leaders in Belgium.
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Canadian Trade Minister says is evident that EU is not now capable of having trade agreement even with Canada. Ouch
A spokesman for the European Commission said that the talks had currently halted, but they were still continuing to work on a deal.
All 28 EU governments support the Comprehensive Economic and Trade Agreement (CETA).
But the bloc cannot approve the deal without support from five sub-federal administrations, and French-speaking Wallonia has steadfastly opposed it.
Britain will conduct Brexit negotiations in a way that will secure it the best deal, the Prime Minister has said after she was questioned over suggestions that the talks should take place in French rather than English.
The EU's lead Brexit negotiator, Michel Barnier, had previously suggested that divorce talks and documents should all be conducted in French.
However, an EU spokeswoman stressed that it was not an official line and that there is "no language regime for the negotiations".
Theresa May's comments came after her first European Council meeting as Prime Minister.
European Commission President said an EU-Canada free trade deal would help end Canadian visa restrictions for Romanians and Bulgarians.Read the full story ›
Britain will consider all options if the atrocities in Syria continue, Prime Minister Theresa May has said.
Speaking after her first European Council meeting, Ms May said she argued for a robust, united message from the EU for the Syrian regime and Russia to stop its attacks on Aleppo.
Prime Minister Theresa May has said Britain will play a "full and active role in the EU" until it leaves.
After leaving the EU Britain will remain "enthusiastic" and "outward looking" and is committed to trading freely with other European countries.
"The UK is leaving the EU, but we are not leaving Europe," Ms May said, speaking after her first European Council meeting.
The Prime Minister said that the UK will continue to argue for free trade and that Britain is discussing trade ties with other countries.
Ms May added she wants to cement Britain as a close partner of the EU once Brexit has taken place and that she is seeking a "mature, cooperative relationship" with the UK's European partners.
Ms May continued that she is not looking to replicate a trade model that another country has with the EU, but that the UK needs its own, and that "the deal that is right for the UK will also be right for the European Union".
However, the MP for Maidenhead did concede that there would be difficult moments as Britain leaves the EU and that it would "take time".
The premier of Belgium's Wallonia region Paul Magnette has told his region's parliament that no breakthrough has been made in talks over the planned EU-Canada free trade deal.
Wallonia maintains that CETA poses a threat to farmers and to welfare standards.
Mr Magnette said talks on Friday had yielded some developments, but pointed out that contention still remains over an independent court system to resolve disputes.
Critics say the court system can be exploited by big business to unduly influence public policy.
CETA is expected to take centre stage is the EU leaders' summit, which is currently underway in Brussels.
A feisty exchange between European Commission President Jean-Claude Juncker and a BBC journalist has signified the tense atmosphere at the EU leaders' summit in Brussels.
Asked about Thursday's dinner with Theresa May and the rest of the EU leaders, an apparently irritated Mr Juncker scoffed before replying: "We had no special event with Theresa May yesterday, she was explaining what her intentions are.
"I will have lunch with her and then we'll see what has to happen."
When pressed by the journalist on what he proposed to discuss with Mrs May, Mr Juncker retorted sternly: "Are you the British prime minister?"
EU leaders have warned that Mrs May faces tough negotiations if she insists on a "hard Brexit".
However, European Council President Donald Tusk has insisted that no formal Brexit talks will be held until Article 50 is invoked.
The president of the European Council has revealed he still wants Britain to be part of the EU.Read the full story ›
- Video report by ITV News Europe Editor James Mates
Theresa May received an initially warm welcome at her first EU summit in Brussels on Thursday, but it didn't stay that way for long.
The President of the European Council, Donald Tusk, told reporters Mrs May was entering a "nest of doves" rather than "the lion's den".
Mr Tusk's welcome was in stark contrast to French President Francois Hollande's, who said: "If Theresa May wants a hard Brexit, then the negotiations will be hard".