Mr Timothy spoke about a “fairly extraordinary” lunch during which Mr Trump shouted at his then-national security advisor Michael Flynn.
“Somebody just mentioned in passing that Vladimir Putin had asked for a call with him, and right in front us he absolutely shouted down Mike Flynn,” he said.
“Like really shouted. This was at a formal dinner with butlers and fancy crockery – and he was properly shouting at him down the table.”
Mr Timothy said the president yelled: “If Putin wants a call with me you just put him through.”
Speaking on the What Were They Thinking? podcast, the former Downing Street figure added: “The whole thing was very a strange experience.
“And not especially reassuring about the state of [Trump’s] mind, or the stability of decision-making in the White House.”
Mr Timothy – No 10 chief of staff between 2016 and 2017 before resigning in the wake of the 2017 general election – also discussed the controversy over Huawei and recent Conservative government attitudes to both the US and China.
Ms May’s senior aide said he was surprised his former boss allowed Huawei a role in developing Britain’s 5G infrastructure, criticising her 2019 decision to approve the Chinese firm as “very, very unwise”.
He described Ms May had been a “Sino-sceptic” during her time in charge at the Home Office and her first year as prime minister.
Mr Timothy also said former chancellor George Osborne had been mistaken in developing a strategy to make Britain “China’s best friend in the West”.
He said: “The problem with that is … you can’t go all in with China without undermining your security relationship with America. China doesn’t share western values, and its strategy is, I’m afraid, one of domination.”
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