The Prime Minister also said she would be “ambitious” in negotiations and backed the UK to be a “global leader in free trade”.
Speaking to reporters in New York, where she has called a summit of US banks to reassure them of the UK’s status post-Brexit, May said the 27 EU nations “will sign up to a deal with us”.
“We will be negotiating with them,” she told the media.
“And as I say 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.
“I believe in good trading relations and I want the UK to be a global leader in free trade.”
Over the weekend, the Visegrad group, or V4 – consisting of Hungary, Poland, Slovakia and Czech Republic – said they would veto agreements if its citizens working and living in Britain were not treated fairly.
Slovak Prime Minister Robert Fico said: “V4 countries will be uncompromising. Unless we feel a guarantee that these people (living and working in Britain) are equal, we will veto any agreement between the EU and Britain. I think Britain knows this is an issue for us where there's no room for compromise.”