The BBC has been accused of cowardice by a writer it selected to give its flagship annual lecture, after it removed his remarks about alleged corruption by Donald Trump.

With the corporation already threatened with a multi-billion lawsuit by the US president, Rutger Bregman, a Dutch author and historian, said the BBC had removed a “key line” from his address when it was broadcast on BBC Radio 4.

Bregman’s claim that Trump was “the most openly corrupt president in American history” was removed from the first of his Reith Lectures, the BBC’s prestigious annual address. The corporation has already received complaints about the decision.

“The BBC has decided to censor my first Reith Lecture,” he said. “They deleted the line in which I describe Donald Trump as ‘the most openly corrupt president in American history’.

“This sentence was taken out of a lecture they commissioned, reviewed through the full editorial process, and recorded four weeks ago in front of 500 people in the BBC Radio Theatre. I was told the decision came from the highest levels within the BBC.”

The BBC is under pressure from the White House after Trump threatened to sue it for up to $5bn (£3.8bn) over an edit of one of his speeches by an edition of Panorama. A row over the edit ultimately led to the resignations of its director general, Tim Davie, and the BBC News chief, Deborah Turness.

The BBC has apologised for the edit, which spliced two parts of Trump’s speech on the day of the Capitol riots in January 2021. However, it is arguing that it did not defame the US president and is not seeking to settle the case with him.

Bregman said he was told a week ago that the claim was being examined by US lawyers, before being told on Monday it would be edited out. The BBC confirmed it removed the comment after seeking legal advice. The lecture is broadcast in the US on the BBC’s World Service.

Davie faced immediate calls to run the full version of the speech.

“At a moment when the defence of free speech and democratic norms is more important than ever, we need the BBC to demonstrate that it will not be cowed by the White House’s bullyboy tactics and tantrums,” writes Anna Sabine, the Lib Dem culture spokesperson, in a letter to the outgoing director general. “I am therefore asking you to broadcast Mr Bregman’s speech in full.”

Bregman, who has previously said the US could be on the verge of an “authoritarian breakthrough”, said the edit of his speech had been made “against my wishes” and left him “genuinely dismayed”.

“Not because people can’t disagree with my words, but because self-censorship driven by fear (Trump threatening to sue the BBC) should concern all of us,” he said. “It’s especially ironic because the lecture is exactly about the ‘paralysing cowardice’ of today’s elites.

“About universities, corporations and media networks bending the knee to authoritarianism. I share this with respect for the many excellent journalists at the BBC. And with the hope that transparency helps strengthen, not weaken, our democratic culture.”

A BBC spokesperson said: “All of our programmes are required to comply with the BBC’s editorial guidelines, and we made the decision to remove one sentence from the lecture on legal advice.”

Approached by the Guardian, Bregman said: “I’m really sad about it. The whole team behind the Reith lectures was incredible.

“And it was such an honour to deliver them, especially because the first Reith lectures in 1948 were delivered by my intellectual hero Bertrand Russell, who was a huge advocate of free speech.

“I still hope lots of people will listen to the lectures. Because it seems to me that the message, about the cowardice of today’s elites, is more relevant than ever.”

Bregman, who sprung to prominence in 2019 with a speech at the World Economic Forum in Davos in which he challenged attenders over tax avoidance, had been invited to give a series of lectures entitled “Moral Revolution”. They were recorded in London, Liverpool, Edinburgh and the US last month.

He later challenged the BBC over its explanation for cutting the corruption remark. “The edit was made at the last minute, after editorial approval and four weeks after the live recording,” he said. “A standard editorial edit doesn’t require days of high-level legal review or the involvement of many people at top level.

“The truth is that the sentence wasn’t inaccurate – it was removed because of legal fears. And that’s exactly the concern my lecture raises: when institutions start censoring themselves out of fear of those in power.”