THERESA May has called for a "mature and co-operative" relationship between Britain and the EU, as she seeks a "smooth" Brexit which she said can be in the interests of both sides.
The British prime minister was speaking at the conclusion of her first European Council summit, at which she was given just five minutes at the end of dinner in the early hours of the morning to set out her position on Brexit.
Her demands for Britain to play a full role in the European Union while it quits the bloc have sparked anger in Brussels, with some senior figures saying it was wrong for the UK to try to shape the future of the EU while it is trying to leave.
In a press conference at the end of the two-day summit, Mrs May said she had made clear that the UK "will continue to play a full and active role within the EU" until the process of withdrawal under Article 50 of the EU treaties is completed.
She said Britain will be "a confident, outward-looking country, enthusiastic about cooperating with our European friends and allies after we leave".
Mrs May said she wanted to "cement Britain as a close partner of the EU once we have left", able to control immigration as well as trading freely with the continent.
She said: "The UK will continue to face similar challenges to our European neighbours, we will continue to share the same values, so I want a mature, cooperative relationship with our European partners.
"I recognise the scale of the challenge ahead. I'm sure there will be difficult moments. It will require some give and take.
"But I firmly believe that if we approach this in a constructive spirit - as I am - then we can deliver a smooth departure and build a powerful new relationship that works both for the UK and for the countries of the EU looking for opportunities, not problems.
"That's in British interests and it's in the interests of all our European partners too."
Mrs May said she wanted to see the completion of the EU's Comprehensive Economic and Trade Agreement (CETA) free trade deal with Canada, which is being held up by opposition in the Walloon regional parliament in Belgium.
But she stressed: "From the UK's point of view, we are not looking to replicate a model that another country has, we are not looking to adopt another model that somebody else has in relation to their trade with the European Union.
"What we want is to develop what is a new relationship for the UK with the EU, to be there when we are outside the EU. What we want is to ensure that we have the right deal for the UK.
"I'm optimistic about that. Obviously, we've got negotiations ahead. Those negotiations will take time, there will be some difficult moments, it will need some give and take.
"But I'm optimistic that we can achieve the deal that is right for the UK, because I actually think the deal that is right for the UK will also be right for the EU."
Mrs May said that apart from issues the remaining 27 members needed to discuss on their own, the UK would continue to play a full role in the bloc.
"As long as we are members of the European Union we will continue to meet our rights and obligations as members of the European Union, and that has been welcome. And that is the right spirit of approach to take to this."
Mrs May made it clear she had been putting Britain's views across at the summit, saying: "I haven't been backwards in coming forwards on issues."
Liberal Democrat leader Tim Farron said: "Given the haphazard way May is dealing with Brexit in her own cabinet, it's not surprising she is struggling to convince other European leaders that this will be anything like the 'smooth withdrawal' her office is briefing.
"Instead of putting the views of a minority of hardline Tory Brexiteers first, our prime minister should be doing what's right for the British people. This means remaining in the single market, maintaining cross-border security and ensuring that Brexit leaves nobody worse off."
