The Mail on Sunday published details of the dispatch from Sir Kim Darroch, despite a warning from Scotland Yard that journalists who released further details of the ambassador's communications could be in breach of the Officials Secrets Act (OSA).
The warning prompted a furious row over press freedom, with Tory leadership contenders Boris Johnson and Jeremy Hunt lining up to defend the right of the media to publish leaked government documents.
The latest memo to be disclosed was said to have been written by Sir Kim in May 2018 following a visit to Washington by Mr Johnson - who was then foreign secretary - in a last ditch attempt to persuade the Trump administration not to abandon the Iran deal.
Under the terms of the agreement - still supported by Britain, France and Germany - international sanctions on Iran were eased in return for Tehran accepting curbs on its nuclear programme.
• READ MORE: Euan McColm: Ambassador episode shows shameful Boris is not fit to leadSir Kim told Mr Johnson: "The outcome illustrated the paradox of this White House: you got exceptional access, seeing everyone short of the president; but on the substance, the administration is set upon an act of diplomatic vandalism, seemingly for ideological and personality reasons - it was Obama's deal.
"Moreover, they can't articulate any 'day-after' strategy; and contacts with State Department this morning suggest no sort of plan for reaching out to partners and allies, whether in Europe or the region."
On Friday, the Metropolitan Police said that it was launching a criminal investigation into the leak to the Mail of Sir Kim's dispatches.
It followed the announcement Sir Kim had decided to quit, saying his position had become "impossible" following the publication of cables in which he described the Trump administration as "inept" and "dysfunctional".
At the same time, Assistant Commissioner Neil Basu issued a warning that any further publication of the cables could constitute a criminal offence and called on journalists to return any leaked government documents.
His comments were roundly condemned by politicians and senior journalists, who accused the Met of the kind of "heavy-handed" approach more usually associated with totalitarian regimes.
In a further statement on Saturday, Mr Basu insisted the Met had "no intention" of trying to prevent the publication of stories in the public interest.
He said the focus of the inquiry by the counter terrorism command - which investigates breaches of the OSA - was "clearly on identifying who was responsible for the leak".
However, he said they had been advised any further publication of the cables "now knowing they may be a breach of the OSA" could also constitute a criminal offence - to which there was no public interest defence.
"We know these documents and potentially others remain in circulation. We have a duty to prevent as well as detect crime, and the previous statement was intended to alert to the risk of breaching the OSA," he said.
In a statement, a spokesman for The Mail on Sunday said it was publishing the latest leaked details - despite the threat of prosecution - because "a free press is vital to our democracy".
"The media must be free to publish such information, in the public interest, as long as it does not endanger lives or national security," the spokesman said.
"Our readers across the globe now have important information about how Britain tried, but failed, to stop President Trump abandoning the Iran nuclear deal.
"What could be more in the public interest than a better understanding of how this position was reached, which may have serious consequences for world peace?"
In response to the latest leak, a Foreign Office spokesman said: 'A police inquiry into the totally unacceptable leak of this sensitive material has begun. The perpetrator 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."