The Labour party has called for the home secretary, Priti Patel, to stand down while a lawyer-led “genuinely independent” inquiry is carried out into bullying allegations against her.

Diane Abbott, the shadow home secretary, suggested the Cabinet Office-led inquiry announced by Boris Johnson into Patel’s behaviour was not sufficiently impartial to restore public trust in the relationship between the government and the civil service.

“It doesn’t necessarily have to cross the Cabinet Office inquiry, but to restore confidence in the respect that the government has for the civil servants we want a genuinely independent inquiry,” Abbott told Radio 4’s Today programme on Tuesday.

“We’ve had other allegations come up overnight and unless you have a conclusive and independent inquiry this thing may run on to the detriment of Priti herself and the government.”

She added: “I’m afraid it would be better if she stood down. We are calling on her to step down while the inquiry goes on.”

Patel’s permanent secretary, Sir Philip Rutnam, quit on Saturday, 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.

On Monday, Patel was also accused of shouting at a former aide with “unprovoked aggression” before removing her from her job. The BBC reported that the aide received a £25,000 government payout after a threatened lawsuit in which Patel was named. The legal correspondence alleges the civil servant took an overdose of prescription medicine shortly after the incident in October 2015.

Diane Abbott: ‘We are calling on her to step down while the inquiry goes on.’ Photograph: Dominc Lipinski/PA

Abbott said the inquiry did not need to be led by a judge, a lawyer could do the job: “Someone who can be seen to be independent”.

Asked if ministers were entitled to order civil servants to do what they wanted, Abbott said: “Ministers have a mandate from the electors, and this government in particular has a very fresh and emphatic mandate, but there is such a thing as a ministerial code and if the allegations against Priti Patel, both by her former permanent secretary and the more recent allegations from the woman who had to be paid off, if they are true she would be in breach of the ministerial code and have to stand down.”

Supporters of Patel say she has been patronised and belittled because of her gender and race.

“This is such a serious issue,” Abbott said. “This is not about things online, or to and fro with interviewers. This is about one of the great departments of state. You cannot have the home secretary at odds with her senior officials in this way.”

Dave Penman, the general secretary of the FDA union, which represents senior civil servants, said on Monday that a cabinet inquiry falls short of the independent inquiry his members have demanded.

“The government is establishing an inquiry that civil servants are expected to have trust in, whilst at the same time ministers stand at the dispatch box and pledge their confidence in the home secretary,” he said.