Deputy Prime Minister Dominic Raab is facing a fresh claim of bullying after an anti-Brexit campaigner alleged he launched an “abusive attack” on her.

Gina Miller said Mr Raab, who was also appointed as Justice Secretary by Rishi Sunak, was “aggressive and intimidating” during an “aggressive encounter”.

A source close to Mr Raab, who denies bullying staff, said her account was “baseless” and “timed to jump on a political bandwagon and give Gina Miller the publicity she craves”.

Meanwhile, the Prime Minister remains under pressure over what he knew about Mr Raab’s behaviour when appointing him deputy.

The Times reported that Cabinet Secretary Simon Case was personally informed of a written complaint against Mr Raab months before his reappointment as Justice Secretary.

Ms Miller, who has launched her own political party, said the Tory MP “launched into an abusive attack on me” while in a BBC studio to debate Brexit in 2016

“I can’t make up my mind if you’re naive, got too much money or just stupid,” she claimed he told her, in an article for the Independent website.

Mr Raab was “furious” when she was told by a young man that a car was ready to pick her up, Ms Miller said, adding that he shouted at the man: “Go get me a f****** car.”

“Raab was aggressive and intimidating, and I was bullied and demeaned,” Ms Miller said.

“This was an aggressive male expressing seemingly misogynistic behaviour. This sort of behaviour is not acceptable from anyone, especially not from a powerful, influential politician.”

A source close to Mr Raab responded: “These are baseless and malicious claims, timed to jump on a political bandwagon and give Gina Miller the publicity she craves.”

Dozens of officials are believed to be involved in the inquiry by senior lawyer Adam Tolley KC which was ordered by Mr Sunak.

Dave Penman, the leader of the FDA union – which represents senior civil servants, has said officials have “suffered mental health crises” as a result of Mr Raab’s behaviour.

“I’ve spoken to people who are civil servants working and have worked for Dominic Raab, who have suffered mental health crises, have lost their careers essentially because they’ve had to move and change jobs,” Mr Penman told Sky News.

Downing Street has only ruled out Mr Sunak being aware of “formal complaints” before appointing Mr Raab, and has not denied he knew about informal allegations.