In the leak of the memos to the Mail on Sunday, Darroch 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," the BBC reported.
He questioned whether the White House "will ever look competent", adding that it was "uniquely dysfunctional" and "divided" under Trump.
He also warned that the US President should not be written off.
Although Darroch said Trump was "dazzled" by his state visit to the UK in June, the Ambassador warned that his administration will remain self-interested, adding: "This is still the land of America First".
Differences between the US and the UK on climate change, media freedoms and the death penalty might come to the fore as the countries seek to improve trading relations after Brexit, the memos showed.
To get through to the President, "you need to make your points simple, even blunt", the Ambassador added.
In response to the leaked memos, the Foreign Office it was "mischievous" but did not deny their accuracy, reports the BBC.
An Office spokesman said the public expects diplomats to provide Ministers with an "honest, unvarnished assessment" of politics in their country.
"Their views are not necessarily the views of ministers or indeed the government. But we pay them to be candid," he said.
The UK embassy in Washington has "strong relations" with the White House and these would continue despite "mischievous behaviour" such as this leak, the spokesman said.
( With inputs from IANS )