Britain must “adapt to the moment and evolve its thinking” to become a global leader in free trade, Theresa May is to say.

The prime minister will pledge to lead the charge in remaking globalisation, days after Donald Trump was elected US president on the promise of protecting American industry and ending a string of free trade agreements.

May’s speech will be seen as an attempt to reposition the UK after the Brexit vote and the US presidential election and as a response to Nigel Farage becoming the first UK politician to meet the president-elect over the weekend.

“Not standing inflexibly, refusing to change and still fighting the battles of the past, but adapting to the moment, evolving our thinking and seizing the opportunities ahead. That is the kind of leadership we need today,” May will tell the lord mayor’s banquet in London.

Her speech follows reports that British ambassador to the US, Sir Kim Darroch, wrote a memo immediately after Trump’s victory that suggested Trump would be “open to outside influence” and that “better relationships” with his team meant that Britain would be uniquely placed to take advantage.

During his election campaign, Trump argued repeatedly that the pursuit of free trade policies had predicated the collapse of homegrown manufacturing industry, bringing cheap consumer goods at the expense of American jobs.

He has since appeared to row back on a number of campaign promises, and in his first TV interview since being elected he told CBS’s 60 Minutes programme on Sunday night there “could be some fencing” in his proposed border wall with Mexico.

Trump said up to 3 million “illegal immigrants” – including those “with criminal records, gang members and drug dealers” – could be deported or jailed after his inauguration in January.

Less than a week after the victory of the real estate billionaire, whose own business dealings have come under repeated scrutiny, May’s speech will warn about the undermining of the social contract when “a minority of businesses and business figures appear to game the system and work to a different set of rules”.

Businesses and governments must change to regain that trust, she is to say, “not just to do business but to do that business in the right way.

“Asking business to work with government to play its part is profoundly pro-business, because it is fundamental to retaining faith in capitalism and free markets. To be the true global champion of free trade in this new modern world, we also need to do something to help those families and communities who can actually lose out from it.”

Britain cannot afford to stand still in the era of such vast and sweeping changes to political orthodoxy, May will say at London’s Guildhall. “So often over our long history, this country has set the template for others to follow.

“We have so often been the pioneer – the outrider – that has acted to usher in a new idea or approach. And we have that same opportunity today.”

The prime minister will say she will be unrepentant in her argument that free markets and free trade are the best remedy for poverty, but that the government “can also do much more to ensure the prosperity they provide is shared by all”.May will say that Britain has an opportunity “to show that our departure from the European Union is not – as some people have wrongly argued – Britain stepping back from the world, but an example of how a free, flexible, ambitious country can step up to a new global role in which alongside the traditional trading blocs; agile nation states like Britain can trade freely with others according to what’s in their own best interests and those of their people.

“This is a new direction – a new approach to managing the forces of globalisation so that they work for all – and it is the course on which the government I lead has embarked.”

May’s speech comes after Farage claimed Trump’s team had raised concerns with him about hostile comments made by British ministers about Trump’s presidential campaign. Boris Johnson, the foreign secretary, and both May’s joint chiefs of staff have also criticised Trump.

Farage met the president-elect for an hour on Saturday night at Trump Tower in New York, posing for a grinning photograph with Trump in front of a pair of ostentatious gold doors. He was the first foreign politician to meet Trump since his election, and the pair discussed returning a bust of Sir Winston Churchill to the Oval Office.

The interim Ukip leader’s offer of serving as a go-between for the UK government and the Trump administration was roundly rebuffed by No 10. A Downing Street source said Farage’s activities in the US were an irrelevance. “We are not using Nigel Farage as a go-between for the very simple reason that he does not represent the government,” the source said. “He is an opposition politician.”

Another government minister said Farage was clearly “on a frolic of his own”, adding that high-level visits were already being planned. “Trump’s knowledge of foreign affairs is not probably his strongest suit, and he may not be fully aware that Farage is not an official member of the government, or representing the UK,” the source said.

The former work and pensions secretary Iain Duncan Smith, a prominent leave campaigner, said Farage was “just trying to get attention” rather than representing British interests.

“This is an ego trip – not a diplomatic one,” Duncan Smith said. “While the PM focusses on sensible, measured diplomacy in Britain’s national interest, all Farage cares about is talking rubbish abroad.”

While some senior Conservatives have indicated that a lack of trust in Farage’s intentions makes a negotiating role impossible, a senior former cabinet minister told the Guardian that the Ukip leader’s help in forging a productive relationship with the new US administration should not be dismissed out of hand. “He is probably the most successful, non-machine party politician the country has seen in a long while,” the source said.

“Frankly, given what the political establishment have said about Trump, any help Nigel Farage is able to give Great Britain with the incoming administration should be welcomed. But the normal machinery of government and diplomacy clearly now kicks in.”

Speaking after the meeting with the president-elect, Farage said: “It was a great honour to spend time with Donald Trump. He was relaxed and full of good ideas. I’m confident he will be a good president. His support for the US-UK relationship is very strong. This is a man with whom we can do business.”

Johnson was absent from an emergency meeting of Europe’s foreign ministers in Brussels on Sunday, which had been called to hash out unified stance on Trump’s election.

Foreign Office sources insisted Johnson believed the meeting was unnecessary since there was a regular meeting of EU foreign ministers on Monday, though his decision not to attend wwould be intended to send a signal that the UK’s loyalty would be to the special relationship rather than the EU.