There will be "difficult" moments in the Brexit negotiations which will require "some give and take," the Prime Minister has said.

Speaking at the end of her first European Council summit, Theresa May said she was seeking a "smooth" exit from the European Union.

She said she was "optimistic" about achieving a deal which was right for the UK and the EU.

In a press conference at the end of the two-day summit in Brussels, May said she has made clear the UK "will continue to play a full and active role within the EU" until the process of withdrawal is completed.

Her demands have sparked anger in Brussels, with some senior figures saying it is wrong for the UK to try to shape the EU's future while trying to leave.

May said Britain will be "a confident, outward-looking country, enthusiastic about cooperating with our European friends and allies after we leave".

She 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.

The Prime Minister 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."

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 currently being held up by opposition in the Walloon regional parliament in Belgium.

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."