The Prime Minister claimed that a good deal for the UK would also benefit the remaining members of the bloc.
She distanced herself from International Trade Secretary Liam Fox’s attack on British business culture as she urged firms to take the opportunities offered by Brexit.
She was speaking after Slovakian leader Robert Fico warned that Britain should expect the negotiation process to be “very painful”.
Mrs May told reporters accompanying her on her visit to the UN General Assembly in New York that a deal would be done and she had previously had constructive talks with Mr Fico.
She said: “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 United Kingdom.
“I think that’s right for us to do that. But I think that a good deal for the UK can also be a good deal for the other member states.
“I believe in good trading relations, I have said I want the UK to be a global leader in free trade.”
She said the Brexit talks were not only about the UK but about trading relationships within the “European arena” as a whole.
Mrs May distanced herself from Dr Fox’s unguarded comments about “fat” and “lazy” British business leaders being more interested in golf than winning export orders.
She said: “We all put things in different ways.”
Mrs May continued: “What Liam is doing is encouraging British businesses to export and that’s an important part of his role as Secretary of State for International Trade. Yes, it’s about trading deals with other countries, which is important as we come to leave the EU, but it’s also about encouraging investment from other countries into the UK and encouraging businesses in the UK to be exporting.
“We have always been a great trading nation, let’s get out there and take the opportunities.”
There are reportedly divisions within the Cabinet over the best approach to Brexit and Mrs May said it was “important to have a range of views” when taking a decision.
“But ultimately we will take a decision collectively as Government as to how best to address these issues and how best to approach them.
“The Exiting the EU Department is the focus of those negotiations, but obviously others around the table all have interests in how those go.
“We are very clear we want to get the right deal for the United Kingdom, that’s for trade in goods and services.”