In a batch of leaked cables, Darroch described Trump as “inept” and "incompetent". Trump said Sunday the ambassador "has not served the UK well".
Downing Street said as quoted by the broadcaster Sky News that Darroch "continues to have the prime minister's full support".
"We have made clear to the US how unfortunate this leak is. The selective extracts leaked do not reflect the closeness of, and the esteem in which we hold, the relationship. At the same time we have also underlined the importance of ambassadors being able to provide honest, unvarnished assessments of the politics in their country", May's spokesperson said.
UK Foreign Secretary Jeremy Hunt said Monday that London would not allow "any interruption" to its "superb relationship" with the United States.