Rishi Sunak was told about Dominic Raab’s “unacceptable behaviour” over the summer before he became prime minister and appointed the deputy PM to his cabinet role, a source has alleged to Sky News.

The source told Sky News’ political editor Beth Rigby that Mr Sunak was made aware of Mr Raab’s conduct but the PM was never “directly told” about specific issues.

Downing Street has said Number 10 officials never advised the PM against appointing Mr Raab.

Asked whether Mr Sunak was made aware of Mr Raab’s “unacceptable behaviour” last summer before he started appointing his top team, the PM’s press secretary said: “The PM was not aware of any formal complaints at the time of appointing Dominic Raab.”

Sunak attacked for how he handled two Tory controversies – politics latest

The press secretary added that she “can’t comment on any private investigations that may or may not have happened” involving Mr Sunak.

Pressed further, she said: “I don’t know what your definition of informal complaints is. The PET (propriety and ethics team) processes are very clear.

“The appointments and usual processes were followed and we were not aware of any formal complaints.”

Mr Sunak has been urged to suspend the deputy prime minister while an investigation into bullying allegations is carried out.

The three permanent secretaries who led officials working under Mr Raab are thought to have given evidence to an inquiry into the deputy PM which is being led by senior lawyer Adam Tolley KC.

A total of eight formal complaints are believed to have been made.

Mr Raab has previously insisted he has “behaved professionally at all times” amid the allegations of bullying and intimidating behaviour.

At Prime Minister’s Questions, Sir Keir Starmer branded Mr Sunak “weak” for keeping Mr Raab in his role.

The deputy PM was sat next to Mr Sunak in the Commons.

Read more: What has led to the deputy prime minister being investigated?

Sir Keir asked the PM if he was “completely unaware of serious allegations of bullying” against the deputy PM before he appointed him.

Mr Sunak replied: “The honourable gentleman ask these questions about what was known and I followed due process, I appointed an independent adviser as soon as I was made aware of new information.”

Probing further, the Labour leader continued: “According to recent reports, some of the complainants were physically sick. One says they were left suicidal.

“How would he feel if one of his friends or relatives was being forced to work for a bully, simply because the man at the top was too weak to do anything about it?”

The PM replied: “When I was made aware of formal complaints I instructed a leading independent KC to conduct an investigation because I take action when these things happen.”

Sky News’ political editor Beth Rigby said the latest source allegation regarding what Mr Sunak knew about Mr Raab’s behaviour “will be worrying for those in Number 10”.

She said recent scandals – including the one involving former Tory chairman Nadhim Zahawi’s taxes – have cut through with the public and by focusing on these, “Sir Keir Starmer is hoping to keep up the appearance that Rishi Sunak’s government is mired in sleaze”.

Yesterday, Jacob Rees-Mogg warned that people are getting “a bit snowflaky” about bullying allegations levelled at government ministers.

The former cabinet minister told Sky News individuals should be “careful” when talking about accusations involving those including Mr Raab.

“It’s a very difficult line to judge. It’s not a straightforward issue in most cases. It’s how did somebody react, what did somebody say, is it reasonable to demand from senior and well-paid professionals a level of good service?” he said.

“And then you have to judge whether that line has been overstepped. But I do worry we are getting a bit snowflaky about this.”

Read more: From Zahawi and Raab to seatbelt gaffe – the U-turns and scandals of Sunak’s first months as PM

Mr Rees-Mogg added that it is “completely sensible” for Mr Raab to remain in his position while the investigation into his conduct continues.

Education Secretary Gillian Keegan told Sky News she disagreed with Mr Rees-Mogg’s comments.

Speaking to Kay Burley this morning, she said: “Well, I mean, I don’t agree with that. Bullying is very serious.”

His remarks were also condemned by a civil service union chief.

Dave Penman, general secretary of the FDA union, said: “Even by Rees-Mogg’s standards this is outrageous.

“A former leader of the House, trivialising bullying that we know has ruined lives and careers.”

Sky News understands Mr Raab has spoken to Mr Tolley once about the allegations but will need to again as they proceed to go through things department by department.

The cut off date for new allegations is understood to have not yet been decided.

The Liberal Democrats have called on the PM to suspend Mr Raab while the investigation into his conduct takes place.

The party’s chief whip Wendy Chamberlain said: “The reported scale of the allegations against Dominic Raab raises real questions for Rishi Sunak. Why hasn’t the prime minister suspended Raab yet, for the duration of this inquiry?”