British Prime Minister Theresa May delivers her speech in Davos | Fabrice Coffrini/AFP via Getty Images UK will be ‘more global’ after Brexit, May tells Davos British PM warns World Economic Forum that many citizens ‘feel that the modern world has left them behind.’

DAVOS, Switzerland — Britain wants “a new leadership role” in the world after Brexit, Theresa May said Thursday, as she warned an audience at the World Economic Forum in Davos that business and governments need to do more to secure “public consent” for globalization.

The U.K. prime minister claimed the British were not turning their back on the world, and had voted to leave the European Union in order to become “even more global and internationalist.”

May, who faced a cool reception in Davos following Tuesday’s hard-hitting speech, in which she confirmed the U.K. would be leaving the European single market, said the world’s political and business elite needed to respond to a “keenly felt sense” among many that the globalized economy was “not working for them.”

“International cooperation is vital. But we must never forget that our first responsibility as governments is to serve the people,” she said. “And it is my firm belief that we — as governments, international institutions, businesses and individuals — need to do more to respond to the concerns of those who feel that the modern world has left them behind.”

She said that Britain outside the EU would become “the strongest and most forceful advocate for business, free markets and free trade anywhere in the world,” and said that China, Brazil and the Gulf states had already “expressed their interest” in striking trade deals. But she also claimed to be delivering a program of reform at home to ensure business and government "spread the benefits" of trade and enterprise to more people.

Her message that Britain’s departure from the EU was not a rejection of multilateralism was met with skepticism by some EU figures present at the speech. “It was a lesson in paradox,” one EU official told POLITICO.

“She’s turned this into a vote for globalization, and they [Britons] voted for the opposite,” another said.

The Dutch prime minister, Mark Rutte, speaking at a panel event in Davos shortly after May’s speech, appeared to reject her characterization of the Brexit vote.

Brexit “means that the U.K. is now making a choice to control migration,” he said, adding that May needed and appeared willing to “accept that there will be a negative impact on growth rate by leaving the single market.”

Speaking to POLITICO during May’s speech in the Davos Congress Hall, Belgian Deputy Prime Minister Alexander De Croo said May’s speech on Tuesday had brought “clarity finally” on Britain’s intentions.

“For the rest, I don’t believe in the [UKIP leader Nigel] Farage rhetoric that the whole EU is now unraveling. It’s not going to happen.”

Responding to May's speech, Cecilia Malmström, the European commissioner for trade, said "it was a good speech. She captured a lot of the concerns of the responsible globalization that we all talk about.”

On U.K starting trade discussions with other governments before leaving the EU, Malmström said: “I know she has. It’s perfectly normal.”