The emails, which could prove highly embarrassing for the Foreign Office, detail Sir Kim Darroch’s assessments of the Trump administration from 2017 to the present.
Officials insisted the relationship with the White House could withstand the “mischievous behaviour” of the leak and defended Sir Kim’s candid style.
The memos, obtained by the Mail on Sunday, suggest that in order to communicate with the president “you need to make your points simple, even blunt”.
In the cache of documents, Sir Kim said: “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.”
He questioned whether the White House “will ever look competent”.
Sir Kim warned that while the president had been “dazzled” by the pomp and ceremony of his state visit in June, his administration would remain self-interested and “this is still the land of America First”.
In one of the most recent documents, Sir Kim refers to “incoherent, chaotic” US policy on Iran and questions Mr Trump’s publicly stated reason for calling off a retaliatory air strike against Tehran following the downing of an American drone.
The US and Iran have been at the brink of armed conflict over tensions in the Gulf, and Mr Trump stated that he called off a planned air strike with minutes to spare because of the potentially high number of casualties.
But Sir Kim said that the explanation “doesn’t stand up” and suggested it may have been motivated by Mr Trump’s focus on the 2020 re-election campaign and his previous promises not to involve the US in foreign conflicts.
“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,” Sir Kim said.
He said it was “unlikely that US policy on Iran is going to become more coherent any time soon” as “this is a divided administration”.
A 2017 letter to the National Security Adviser Sir Mark Sedwill, sent 150 days into the Trump administration, laid bare the trouble in the White House.
Media reports of “vicious infighting and chaos” were “mostly true” despite the president’s attempts to brush them off.
Referring to the early allegations of collusion between the Trump campaign and Russia, the memo said “the worst cannot be ruled out”.
A lengthy investigation by Robert Mueller published earlier this year cleared the Trump team of the collusion allegations.
A Foreign Office spokesman said: “The British public would expect our ambassadors to provide ministers with an honest, unvarnished assessment of the politics in their country.
“Their views are not necessarily the views of ministers or indeed the Government.
“But we pay them to be candid. Just as the US ambassador here will send back his reading of Westminster politics and personalities.
“Of course we would expect such advice to be handled by ministers and civil servants in the right way, and it’s important that our ambassadors can offer their advice and for it remain confidential.
“Our team in Washington have strong relations with the White House and no doubt… these will withstand such mischievous behaviour.”