Dominic Raab will face an investigation into two formal complaints against him after the Prime Minister agreed to his request for an independent inquiry.

The Deputy Prime Minister confirmed on Wednesday that two separate complaints had been made about his conduct, as he asked the Prime Minister to open an independent investigation into the allegations.

Mr Sunak told the Justice Secretary that “integrity, professionalism and accountability are core values of this Government” and in letter to his deputy said that an investigation was the “right course of action”.

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

He tweeted on Wednesday that he had “written to the Prime Minister to request an independent investigation into two formal complaints that have been made against me”.

“I look forward to addressing these complaints, and continuing to serve as Deputy Prime Minister, Justice Secretary, and Lord Chancellor,” he said.

Mr Sunak, who is in Indonesia at the G20 summit, appeared to continue to stand by Mr Raab, who will be in the spotlight almost immediately when he deputises for him at Prime Minister’s Questions later on Wednesday.

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”.

Top Ministry of Justice officials had reportedly ruled there must be a senior civil servant in the room at all meetings involving Mr Raab due to the recent allegations, according to The Guardian on Wednesday.

The newspaper also reported that Philip Rycroft, the former permanent secretary to the Department for Exiting the European Union, raised concerns about Mr Raab’s behaviour during his time as Brexit secretary with the then-cabinet secretary Mark Sedwill.

Mr Raab was also reportedly warned about his behaviour towards officials while he was foreign secretary.

The concerns were raised with Mr Raab by Lord Simon McDonald, who was the senior civil servant at the Foreign Office, and the mandarin also informally discussed the situation with the Cabinet Office’s propriety and ethics team, The Guardian reported.

The Deputy Prime Minister, in his letter to Mr Sunak, said he had been “blessed to work with a wide range of outstanding civil servants, in particular my brilliant and dedicated private offices”.

“I have always welcomed the mutual challenge that comes with serious policy-making and public service delivery.

“I have always sought to set high standards and forge teams that can deliver for the British people amidst the acute challenges that we have faced in recent years.

“I have never tolerated bullying, and always sought to reinforce and empower the teams of civil servants working in my respective departments.”

In a radio interview on Monday, Lord McDonald had acknowledged that allegations Mr Raab could be a bully were plausible.

Asked by LBC radio if characterisation of Mr Raab as someone who could bully and around whom bullying could happen, he replied: “Yes.”

Lord McDonald added: “Dominic Raab is one of the most driven people I ever worked for, he was a tough boss.

“Maybe they are euphemisms, but I worked closely with him and I didn’t see everything that happened.”

It is the latest blow to the new prime minister’s administration, after he faced criticism for appointing Sir Gavin Williamson to his senior team despite being told he was under investigation for allegedly bullying a colleague, claims that caused Sir Gavin to quit.