Theresa May has told global business leaders that their companies must pay more in tax and less to their executives or face being caught by a surge in populism.

In a powerful critique of business delivered at the World Economic Forum in Davos, the prime minister said that multinational companies could no longer afford to play “by a different set of rules to ordinary working people”. This meant businesses paying their fair share of tax, recognising their obligations and duties to their employees, and trading with smaller companies “in the right way”, she said.

Mrs May added that unless businesses responded to these issues, the forces of liberalism, free trade and globalisation that they all took for granted would be “called into question”.

“Across Europe parties of the far left and the far right are gathering support by feeding off an underlying and keenly felt sense among some people — often those on modest to low incomes living in relatively rich countries around the West — that these forces are not working for them,” she said. “And those parties, who embrace the politics of division and despair, feed off the sense among the public that mainstream political and business leaders have failed to comprehend their legitimate concerns for too long.”

She also urged businesses to provide greater accountability to shareholders.

Mrs May said that governments could not win the fight against populism alone.

Business needed “to spread the benefits” because too many people felt “left behind”. “If we are to make the case for free markets, free trade and globalisation, we must face up to the concerns people have and demonstrate the capacity to deliver for all,” she said.

“Business must show that everyone plays by the same rules. It means everyone paying their fair share of tax, recognising their obligations and duties to their employees and supply chains. All of us taking steps to address executive pay.”

Seizing the Leave campaign mantra, she added: “We have to step up and take control to make sure free trade and globalisation work for everyone.”

She invoked Britain’s long history of internationalism as she sought to change the narrative around Brexit. She characterised those who voted to leave the EU as people who “chose to build a truly global Britain”.

European politicians took issue with her threat to turn the UK into a tax haven if negotiations fail, though.

Wolfgang Schäuble, Germany’s finance minister, said that slashing taxes would undermine Mrs May’s vision of “a truly global” Britain. He said: “The UK has always agreed we will not use tax as an instrument for competition.”

Mrs May also defended Boris Johnson after the foreign secretary compared the president of France to a Second World War camp guard. The prime minister insisted that Mr Johnson had been making the same argument that she had made in her landmark Brexit speech this week.

She told the BBC: “The point that Boris was making was that, actually, it is in the interests of the countries who will remain in the European Union, and in the interests of the United Kingdom, to get a good trade deal, a trade deal that ensures we see the least possible disruption to our economies.”

The EU trade commissioner Cecilia Malmström said that Britain was at the bottom of the queue when it came to negotiating a trade agreement. “We are negotiating 15-16 trade deals at the moment so we are busy,” she said.

Simon Collins, UK chairman of KPMG, was among business leaders who welcomed Mrs May’s speech. “The prime minister has sent a clear signal of intent to build on Britain’s heritage as a strong multicultural trading nation and establish the country as the global leader of free trade,” he said. Business leaders should “stop hand-wringing” and “start an action plan”, he added.