A complaint against Dominic Raab alleges that he oversaw a “perverse culture of fear” at the Ministry of Justice, according to reports.

The contents of the complaint were revealed by the Times newspaper on Thursday, a day after the Prime Minister agreed to open an independent investigation into the Justice Secretary on his request after two formal complaints were made against him.

The newspaper quotes from the complaint, reportedly initially submitted by a group of mid-ranking officials in March before being re-submitted this week as a formal complaint.

The letter of complaint, according to the Times, references a “perverse culture of fear” and describes his communication style as “often abrupt, rude and can be upsetting”.

“There have been multiple recent examples of colleagues being left in tears after being on the receiving end of this inappropriate behaviour.

“We are extremely worried about the perverse culture of fear that is clearly permeating this department… We are proud of the work we do here, but the tangible shift towards a dysfunctional working culture is starting to hinder that”, the complaint says.

“The combination of the pressure of work and unreasonable deadlines has had such an impact on some colleagues’ mental and physical health that they have visited their GPs, and some have subsequently been signed off work for extended periods of time. Colleagues have confided in [each other] that they have been reluctant to be signed off due to the impact that this would have on their other team members,” according to the letter.

Mr Raab told the Commons on Wednesday that he was “confident” he has behaved “professionally”, with Downing Street saying that Mr Sunak still has full confidence in his deputy.

Mr Raab has been facing a series of allegations he bullied officials and deployed rude and demeaning behaviour in previous Cabinet roles.

In a letter to Mr Raab on Wednesday, Mr Sunak told the Cabinet minister that “integrity, professionalism and accountability are core values of this Government” and said that an investigation was the “right course of action”.

In his letter to the Prime Minister, Mr Raab said: “I have just been notified that two separate complaints have formally been made against me, in parallel, from my time as foreign secretary and my first tenure as justice secretary, which ended in September of this year.

“I am, therefore, writing to request that you commission an independent investigation into the claims as soon as possible. I will co-operate fully and respect whatever outcome you decide.”

The Conservative MP for Esher and Walton told Mr Sunak he had “never tolerated bullying, and always sought to reinforce and empower the teams of civil servants working in my respective departments”.

Downing Street said that work has begun to appoint the investigator, who will be someone from outside the Government, but would not say when the person would be in post or when the inquiry would be completed.

A source close to Mr Raab said it would be inappropriate to comment on allegations now an investigation has been confirmed.