"The administration is set upon an act of diplomatic vandalism, seemingly for ideological and personality reasons – it was Obama's deal," Ambassador Kim Darroch wrote in a diplomatic cable in May 2018.
"The outcome illustrated the paradox of this White House: You got exceptional access, seeing everyone short of the president," he wrote.
Darroch announced his resignation on Wednesday after the Mail published cables in which he'd branded the Trump administration “dysfunctional” and “inept.”
He said it was now "impossible" to do his job.
The White House responded by refusing to deal with him, and Trump branded the ambassador a "pompous fool" in a Twitter fusillade.
UK police have warned journalists that publishing the documents "could also constitute a criminal offense", sparking widespread condemnation.
Yet both Boris Johnson and Jeremy Hunt, the two contenders to become Britain's next prime minister, have defended the media's right to publish.
The Sunday Times reported that a government investigation into the leak had identified a civil servant as the person responsible.
Working with officials from the National Cyber Security Centre, part of spy agency GCHQ, and MI6, the probe has homed in on a suspect who had access to historical Foreign Office files, the paper said.
In May 2018, Britain's then-foreign minister Johnson went to Washington to try to persuade Trump not to abandon the Iran deal.
In a cable sent afterward, Darroch reportedly indicated there were divisions in Trump's team over the decision, and criticized the White House for a lack of long-term strategy.
"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," he wrote.
He reported back that Secretary of State Mike Pompeo, during his talks with Johnson, "did some subtle distancing by talking throughout about 'the president's decision.'"
The newspaper reported that, according to Darroch, Pompeo also hinted that he had tried but failed to "sell" a revised text to Trump.
In 2015, the United States, China, Britain, France, Russia and Germany signed a deal with Iran to limit its nuclear program in exchange for a partial lifting of international economic sanctions.
Trump had long been critical of the deal and withdrew the United States on May 8, 2018.
AFP and AP contributed to this story.