The memo, written by Britain's former ambassador to the US Kim Darroch, said the decision to abandon the Joint Comprehensive Plan of Action (JCPOA) was a "diplomatic vandalism," according to the Daily Mail newspaper.
"The administration is set upon an act of diplomatic vandalism, seemingly for ideological and personality reasons it was Obama's deal," Darroch wrote in a diplomatic telegram in May 2018, reported Xinhua news agency.
The memo was written shortly after then British Foreign Secretary Boris Johnson's trip to Washington to persuade the White House to stick with the nuclear deal, the newspaper said.
In the cable, Darroch indicated there were divisions among Trump's advisors and said the White House lacked a "day-after" strategy on what to do after the withdrawal from the JCPOA.
"Moreover, they can't articulate any 'day-after' strategy; and contacts with the State Department this morning suggest no sort of plan for reaching out to partners and allies, whether in Europe or the region," Darroch wrote.
The report has come amid a growing diplomatic rift between the two allies.
Last week, the first batch of leaked memos published by British media showed that Darroch described the Trump administration as "inept" "dysfunctional" and "faction riven," prompting the ambassador's resignation.
In an angry response on Twitter, Trump claimed Darroch was a "pompous fool," saying the US "will no longer deal with" him.
The British authorities have launched an investigation to find the person responsible for the leak. According to the Sunday Times, which cited anonymous official sources, a suspect had been identified and the case was related to a computer hack.
( With inputs from IANS )