May (left) with German chancellor Angela Merkel. Reuters/Hannibal Hanschke Theresa May does not appear to be worried by the threats made by EU member states to block Brexit.

Over the weekend, it was reported that a key group of states in eastern Europe was promising to veto any Brexit deal which would damage the rights of their citizens to live and work in the United Kingdom.

Slovakian Prime Minister Robert Fico said: “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... this is an issue for us where there’s no room for compromise."

May, though, isn't concerned by the threats. Speaking as she travelled to New York for a UN General Assembly meeting, she said all 27 EU states would agree to the Brexit deal Britain wants.

"The 27 will sign up to a deal with us," she said. "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."

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

Brits voted to leave the Union in the June 23 referendum. Since then, the main talking point has been how difficult negotiating the country's official departure from the EU could be for May's government given the refusal of European leaders to compromise on key issues.

Both European Commission President Jean-Claude Juncker and the EU Parliament's chief Brexit negotiator Guy Verhofstadt have said on numerous occasions that Britain will not be able to opt-out of the free movement of people agreement if it wishes to retain access to the single market.

This is the sort of Brexit deal May and ministers like foreign secretary Boris Johnson have said they would like to secure. The British government is under pressure from pro-Brexit politicians and Leave voters to strike a deal that will significantly reduce the number of migrants entering the country.

May's remarks represent the first time she has really spoken out against the many warnings issued to Britain by European leaders. It will be received well by members of her party who want Britain to be tough and confident during Brexit negotiations, but whether they remain patient while the government dithers over the process of leaving remains to be seen.

May has already said that she will not trigger Article 50, the clause that will formally begin the process of leaving the EU, until 2017 at the earliest.