British Prime Minister Theresa May has dismissed threats by some EU countries to veto Brexit negotiations with the UK and stressed that all 27-member states will sign up to a deal with Britain.

Her comments came after Slovakian prime minister Robert Fico yesterday said that four central European countries Slovakia, Poland, the Czech Republic and Hungary were willing to block talks unless their citizens retained their rights to work in the UK after the country voted to leave the European Union in a referendum on June 23.

"The 27 will sign up to a deal with us. We will be negotiating with them. We will be ambitious in what we want to see for the UK. A good deal for the UK can also be a good deal for the other member states because I believe in good trading relations and I have said I want the UK to be a global leader in free trade," May said yesterday just before she flew out to New York to attend the UN General Assembly session.

"This is not just about us, it’s actually about their relationships and trading within that European arena," she added.

Fico had said that member states intend to make it "very difficult for the UK" and said Britain is "bluffing" when it says it can get a good Brexit deal.

"I had very constructive meetings with [Mr Fico] when I was doing my visits earlier in the summer. I’ve said what I want to see is the deal that’s right for the UK. I think that will also be a deal that’s good for the member states of the European Union," May said.

May is accompanied on the trip by her Indian-origin minister for international development Priti Patel and UK foreign secretary Boris Johnson.