A diplomat representing Donald Trump lobbied the UK on behalf of the jailed far-right activist known as Tommy Robinson and threatened to publicly criticise its handling of the case, it has been reported.

Sam Brownback, the US ambassador for international religious freedom, is alleged to have raised concerns over Robinson’s safety in prison with the British ambassador in Washington, according to Reuters, which cited three sources.

It was unclear why an official responsible for religious freedom would intervene on behalf of the founder of the English Defence League, which has organised violent protests against Muslim immigrants over the past decade. Robinson, whose real name is Stephen Yaxley-Lennon, has recently styled himself as a journalist and campaigner against Islamic fundamentalism.

He was arrested in late May after broadcasting an hour-long video via Facebook from outside Leeds crown court during a trial related to child molestation. He was sentenced to 10 months’ jail for contempt of court and a further three months for breaching the terms of the previous suspended sentence.

The case has become something of a cause célèbre for the “alt-right” in the US, where activists have defended Robinson’s right to freedom of expression. In May, the president’s son, Donald Jr, retweeted one of Robinson’s supporters, adding: “Don’t let America follow in those footsteps.”

On Friday, Charlie Kirk, a prominent Trump supporter and founder of the conservative student organisation Turning Point USA, attacked the mayor of London in a tweet that said: “Sadiq Khan is trying to lecture the world on ‘free speech’ while Tommy Robinson is locked in a London prison for speaking his mind.”

The Middle East Forum, a conservative US thinktank, said it had sponsored and organised the “Free Tommy Robinson” demonstration in London near parliament on Saturday in collaboration with British and European groups.

Reuters said its report was based on information from a British official and two sources close to the organisers of the pro-Robinson demonstration.

It said the British official claimed that Brownback, a former senator and governor of Kansas, raised the case last month with Kim Darroch, the British ambassador to the US, during a meeting that covered a range of “religious freedom issues”.

“Brownback allegedly told Darroch that if Britain did not treat Robinson more sympathetically, the Trump administration might be compelled to criticise Britain’s handling of the case, according to the two sources in contact with organisers of the planned pro-Robinson demonstration,” Reuters reported.

“The sources allegedly said Robinson’s supporters, who have also reportedly been in touch with the Trump administration about the issue, were concerned that he could be attacked by other prisoners.”

On Saturday the anti-racism group Hope Not Hate tweeted the US president: “Hey @realDonaldTrump — your ambassador has been lobbying for Tommy Robinson, a criminal lowlife and convicted fraudster, who assaulted a woman police officer.”

A US state department spokesman said the “characterisations” of Brownback’s meeting with Darroch were “completely false”. The Foreign Office in London and the British embassy in Washington did not comment.