Investors should threaten to pull their funds from tech giants such as Facebook and Twitter if they fail to remove terrorist propaganda, Theresa May will tell the Davos economic summit.

The Prime Minister will step up her battle against social media firms blamed for failing to act to stop the spread of extremist content – arguing shareholders have the power to “make a big difference”.

Speaking to world leaders in the Swiss mountain resort, Mrs May will point to the example of the messaging platform Telegram, which has bowed to pressure to censor extremist content.

And she will praise shareholders of Facebook and Twitter, who recently demanded an end to secrecy about sexual harassment, fake news and hate speech on their sites.

“Investors can make a big difference here by ensuring trust and safety issues are being properly considered. And I urge them to do so,” the Prime Minister will say.

The speech will see Mrs May again increasing pressure on technology firms, which have been blamed for provoking people to carry out terror attacks.

Last year, she challenged them to take down terrorist propaganda in as little as one hour and to develop technology to prevent “evil material” ever appearing on the web.

If they fail to act, the Government would consider the threat of fines, she threatened – a step already taken by Germany, which passed a law last June.

In Davos, Mrs May is expected to say: “These companies simply cannot stand by while their platforms are used to facilitate child abuse, modern slavery or the spreading of terrorist and extremist content.”

But she will also turn the focus on investors, saying: “We also need cross-industry responses because smaller platforms can quickly become home to criminals and terrorists.

“We have seen that happen with Telegram. And we need to see more cooperation from smaller platforms like this. No one wants to be known as ‘the terrorists’ platform’ or the first-choice app for paedophiles.

“Second, investors can play a vital role by considering the social impact of the companies they are investing in. They can use their influence to ensure these issues are taken seriously.

“For example, earlier this month a group of shareholders demanded that Facebook and Twitter disclose more information about sexual harassment, fake news, hate speech and other forms of abuse that take place on the companies’ platforms.”

Mrs May will also stress her determination to establish the UK as a world leader in artificial intelligence, arguing it has revolutionary potential.

“Right across the long sweep of history, from the invention of electricity to the advent of factory production, time and again initially disquieting innovations have delivered previously unthinkable advances and we have found the way to make those changes work for all our people,” she will argue.

Mrs May arrived in Davos on Wednesday evening when she held a face-to-face meeting with the Swiss President.

After her speech on Thursday, she will stage her much-prized talks with Donald Trump, which No 10 said would focus on “discussions about foreign affairs”.

Downing Street insists it is relaxed about the President choosing Emmanuel Macron as the first leader to be invited to the US on a state visit – a sign of the surprising rapport between the two leaders.

In contrast, his relations with Mrs May have been strained, after they clashed over Mr Trump’s reposting of anti-Muslim tweets by the far-right Britain First group.