Britain's ambassador in the US has described President Donald Trump and his administration as "inept" and "uniquely dysfunctional," according to leaked diplomatic memos published by the Mail on Sunday.

Ambassador Kim Darroch reportedly said Trump's presidency could "crash and burn" and "end in disgrace," in the cache of secret cables and briefing notes sent back to Britain seen by the newspaper.

"We don't really believe this administration is going to become substantially more normal; less dysfunctional; less unpredictable; less faction riven; less diplomatically clumsy and inept," Darroch allegedly wrote in one dispatch.

The paper said the most damning comments by Darroch described Trump, who was received by Queen Elizabeth II during a state visit to Britain just last month, as "insecure" and "incompetent."

A memo sent following the controversial visit said that the president and his team had been "dazzled" by the visit but warned Britain might not remain "flavour of the month" because "this is still the land of America First."

He reportedly wrote that the "vicious infighting and chaos" inside the White House - widely reported in the US but dismissed by Trump as "fake news" - was "mostly true."

Darroch is one of Britain's most experienced diplomats whose posting in Washington DC began in January 2016, prior to Trump winning the presidency.

The Mail on Sunday said the memos, likely leaked by someone within Britain's sprawling civil service, cover a period beginning in 2017.

In one of the most recent reported dispatches filed on June 22 Darroch criticized Trump's fraught foreign policy on Iran, which has prompted fears in global capitals of a military conflict, as "incoherent" and "chaotic."

He allegedly said the president's assertion, that he called off retaliatory missile strikes against the Iranian regime after a US drone was shot down because it risked killing 150 Iranians, "doesn't stand up."

"It's more likely that he was never fully on board and that he was worried about how this apparent reversal of his 2016 campaign promises would look come 2020," Darroch reportedly stated, referring to the next presidential election.

Britain's Foreign Office did not dispute the veracity of the memos. "The British public would expect our ambassadors to provide ministers with an honest, unvarnished assessment of the politics in their country," a spokeswoman said.