Boris Johnson has given a green light to ministers who wish to smear the reputations of top civil servants, a union leader has claimed, as a further allegation of unacceptable behaviour against the home secretary, Priti Patel, emerged on Sunday night.

Following explosive claims from her former permanent secretary, Sir Philip Rutnam, that Patel lied and bullied staff, Dave Penman, the head of the senior civil servants union, the FDA, said that the prime minister and his closest aides have “ripped up the rule book” that ensured the ministers do not attack civil servants.

Penman said the use of unattributable comments and smears against Rutnam were part of a campaign by No 10 to undermine senior mandarins.

“Civil servants need to be able to give ministers impartial, evidence-based, professional advice. Whilst that is not always welcome, it is essential for good government.

“The concern will be that if this advice is viewed as inconvenient or obstructive, then unattributable briefings will ensue. As we’ve seen with this latest episode, that can be both highly personal and career-threatening.

“What we are witnessing now is becoming a new norm. It’s also increasingly clear that this modus operandi is being led by No 10 and those around the prime minister,” he said.

Rutnam quit on Saturday after accusing Patel of orchestrating a “vicious” campaign against him, of lying about her involvement in it and of creating a climate of fear in her department.

He plans to take his case to an employment tribunal, which could call Patel, Johnson and Dominic Cummings, the prime minister’s chief aide, as witnesses.

Amid mounting pressure upon the home secretary to step down, the BBC claimed that another formal complaint about Patel was made when she was an employment minister at the Department for Work and Pensions between 2015 and 2016.

The alleged complaint was made by a member of her private office – a team of six to eight civil servants that works closely with an individual minister. A spokesman for Patel did not respond to a request for a comment from the Guardian.

Patel could well face questions in parliament about her behaviour. The Labour leadership candidate Keir Starmer called on the home secretary to address the explosive allegations when parliament resumes on Monday.

“The home secretary has a duty to come to parliament on Monday to explain the allegations made about her own conduct,” Starmer said.

He has also called for the cabinet secretary, Sir Mark Sedwill, to launch an immediate investigation into the circumstances surrounding Rutnam’s departure.

Asked if Patel could stay in post, the shadow chancellor, John McDonnell, told Sky’s Sophy Ridge programme: “I can’t see it, it’s bizarre.”

The row comes two weeks after Sajid Javid quit as chancellor when Johnson ordered him to fire his team of aides.

In an unprecedented statement from a top civil servant, Rutnam said on Saturday the campaign against him included “false” claims that he had briefed the media against the home secretary.

“The home secretary categorically denied any involvement in this campaign to the Cabinet Office. I regret I do not believe her. She has not made the effort I would expect to dissociate herself from the comments.

“Even despite this campaign I was willing to effect a reconciliation with the home secretary. But despite my efforts to engage with her, Priti Patel has made no effort to engage with me to discuss this.

“I believe these events give me very strong grounds to claim constructive, unfair dismissal and I will be pursuing that claim in the courts,” he said.

Rutnam said his experience shows a wider pattern of behaviour in Whitehall. “One of my duties as permanent secretary was to protect the health, safety and wellbeing of our 35,000 people.

“This created tension with the home secretary, and I have encouraged her to change her behaviours. I have received allegations that her conduct has included shouting and swearing, belittling people, making unreasonable and repeated demands – behaviour that created fear,” he said.

Allegations that Patel bullied staff emerged 11 days ago in the Times, which claimed she had been accused of belittling officials in meetings, making unreasonable demands and creating an “atmosphere of fear”. The Guardian disclosed that she was accused of emerging from an office saying: “Why is everyone so fucking useless?”

Over the subsequent 10 days, Rutnam claims he was briefed against across the media by sources said to be from either No 10 or friends or allies of Patel. He was accused of being unable to do his job, of being undeserving of his pension, and was compared to Eeyore, the negative, ponderous donkey character from AA Milne’s Winnie the Pooh stories.

The Cabinet Office tried to negotiate a leaving package including a payoff for Rutnam if he left the department quietly. But the negotiations broke down late on Friday night.

A Cabinet Office spokesperson said: “We take all allegations of misconduct seriously. We do not comment on individual personnel matters and note Sir Philip’s intentions to bring legal action against the government, it would therefore be inappropriate to comment any further at this time.

“We are committed to delivering this government’s agenda, and an interim permanent secretary has been appointed to ensure the vital work of the Home Office continues uninterrupted.”

Johnson on Sunday led a number of senior Tories in backing Patel, who has denied she mistreated staff. Speaking during a visit to Public Health England in north London, Johnson said he “absolutely” had confidence in her.

“I think she’s a fantastic home secretary … Anybody who’s been home secretary will testify that is one of the toughest jobs in government,” he said.