According to the Daily Mail Saturday, the former ambassador said Trump seemed to be discarding the Iran nuclear deal for "personality reasons," as the deal had been agreed to by former President Barack Obama. The paper also reported that Darroch hinted at discord brewing between Trump's closest aides and said the White House had failed to produce a "day-after" plan on how to handle the aftermath of withdrawing from the deal.
CNN has not seen the leaked cables and cannot confirm their contents.
The White House told CNN it has no comment on the story.
A UK Foreign Office spokesman told CNN on Saturday that whoever leaked the cables "should face the consequences of their actions."
"It's not news that the US and UK differ in how to ensure Iran is never able to acquire a nuclear weapon; but this does underline that we do not shy away from talking about our differences and working together," the spokesman said. "That is true of the current tensions in the Gulf where we, the UK, are in close contact with our American and European allies to de-escalate the situation."
Basu's statement caused concern over press freedom in the UK after he controversially warned journalists that publishing leaked government documents may lead to a criminal prosecution.
However on Saturday the assistant commissioner released an updated statement, reiterating that the police force "respects the rights of the media and has no intention of seeking to prevent editors from publishing stories in the public interest in a liberal democracy."
Meanwhile, Isabel Oakeshott -- the journalist behind the Mail on Sunday stories based on the leaked diplomatic telegrams -- confirmed on Twitter that she is dating the chairman of the Brexit Party, but adding that "he had nothing to with my story."
He "has never seen the cables and doesn't know the identity of the source," Oakeshott wrote in response to newspaper reports that she was dating Richard Tice.
"So what? It is not a secret," she wrote Sunday.
Tice, for his part, also rejected suggestions he was angling to replace Darroch.
"Conspiracy theorists who think I want US Ambassador job totally wrong. Ridiculous suggestion! But other senior pro Brexit businessperson [sic] would do great job promoting U.K. & securing quick trade deal," he tweeted.
After Trump pulled out of the Iran deal in 2018, the US imposed new sanctions that have crippled the Iranian economy, which now exports less than half of the oil it did before the new round of sanctions.
On the campaign trail, Trump repeatedly denounced the Iranian nuclear agreement as "the worst deal ever."
CNN's Richard Allen Greene, Larry Register, Jamie Crawford, Michelle Kosinski, Schams Elwazer, Stephen Collinson, Bianca Britton, Max Foster, Peter Bergen, Lauren Said-Moorhouse and Nina dos Santos contributed to this report.