Senior politicians, a former cabinet secretary and an ex-head of the home civil service have called for a top-level inquiry into how Boris Johnson’s closest aide, Dominic Cummings, was able to sack an adviser to Sajid Javid, the chancellor of the exchequer, without Javid’s knowledge and then order an armed police officer to escort her out of Downing Street in front of staff.

A former senior Metropolitan police officer, former Chief Superintendent Dal Babu, also said the episode should be subject to urgent twin investigations by the cabinet secretary, Mark Sedwill, and Scotland Yard.

The demands for inquiries into the sacking last Thursday of Sonia Khan, the 27-year-old Treasury special adviser, came amid heightened tension at Westminster over Johnson’s decision to suspend parliament for five weeks.

The suspension, planned by Cummings for several weeks, was partly designed to limit the time MPs will have to block a no-deal Brexit.

Saturday’s demonstrations against the shutting down of parliament featured protesters across the country chanting “stop the coup” and “save our democracy”.

Cummings is understood to have concluded that Khan had been dishonest about her recent contacts with her ex-boss, the anti-no deal former chancellor Philip Hammond, and one of his ex-aides – accusations that Khan strongly denies.

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Having summoned her to No 10 on Thursday evening to question her, Cummings took her two phones, one used for private calls and one for work, and fired her after seeing she had talked to an ex-aide to Hammond last week. Cummings then went outside No 10 and asked an armed officer to enter the building and escort Khan off the premises.

Friends of Khan said she was deeply upset by the episode and was considering what action to take next. They accused Cummings of establishing a “reign of terror” at the heart of government.

Hammond is heavily involved in attempts by a cross-party group of MPs to prevent a no-deal Brexit by passing legislation when MPs return to Westminster this week. They hope a new law can be passed mandating Johnson to ask the EU for a further extension to the UK’s membership if the prime minister cannot strike a deal soon.

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On Saturday Hammond condemned “staggeringly hypocritical” plans to withdraw the whip from Conservative MPs if they vote against the government’s policy on Brexit. In a tweet, he said: “If true, this would be staggeringly hypocritical: 8 members of the current cabinet have defied the party whip this year. I want to honour our 2017 manifesto which promised a ‘smooth and orderly’ exit and a ‘deep and special partnership’ with the EU. Not an undemocratic No Deal.”

On Friday, Javid confronted Johnson in a heated meeting and demanded an explanation into how the volatile Cummings had dismissed one of his staff without telling him beforehand.

Former attorney general Dominic Grieve told the Observer that if the accounts of the sacking, not denied by Downing Street, were true, it was an outrageous abuse of power by Cummings and inappropriate of the police to have got involved. “If the facts are correct Mr Cummings’s behaviour in inviting the police into what at most could only have been an employment issue is deeply troubling. It was wrong of the police to get involved.”

He said the prime minister needed to explain why “ordinary principles of fair behaviour have broken down in his office, and hold an inquiry by the cabinet secretary”.

Yvette Cooper, the Labour chair of the House of Commons home affairs select committee, said: “Government advisers must not abuse their power by drawing the police into heavy- handed political stunts. This needs to be reviewed by the cabinet secretary and the Metropolitan police straight away.”

Former cabinet secretary Lord Turnbull said it was up to No 10 to explain under what authority Cummings had been working when he dismissed a fellow special adviser and why he thought he had the right to ask an armed officer to march her out of Downing Street. “Getting one of the armed police to escort an adviser out of Downing Street is deeply offensive and is part of Cummings’s mantle of fear,” he said.

The former head of the home civil service, Lord Kerslake, also called for an urgent inquiry by the cabinet secretary.

Before parliament’s return on Tuesday, when MPs from all opposition parties will try to block a no-deal Brexit, Labour leader Jeremy Corbyn on Saturday accused Johnson of mounting a “smash and grab raid on our democracy” to force through no-deal Brexit.

Writing in the Observer Corbyn said Johnson “is running scared of being held to account” and calls for a general election in which Labour would commit to another Brexit referendum.

“A general election is the democratic way forward. And in that election Labour will give the people the chance to take back control and have the final say in a public vote, with credible options for both sides, including the option to remain.”

Dal Babu who served in the Met for 30 years said that police officers should not have been asked to march Khan out of Downing Street. “It’s a shocking abuse of armed officers, it’s appalling. The police should be asking questions of Cummings, asking questions of the prime minister around an abuse of process. At a time when we should be proud of having BAME women at the heart of government this sends out a very wrong signal of how people are valued.

“I would expect the cabinet secretary Mark Sedwill to conduct an inquiry and I would expect the police to conduct an inquiry about individuals in No 10 utilising police officers in a very inappropriate way.”