Priti Patel is facing demands from opposition politicians to announce a statutory inquiry into failings that allowed a serving Metropolitan police officer to kidnap, rape and murder Sarah Everard.

After announcing that an investigation would examine why Wayne Couzens had not been identified by the force as a sexually aggressive predator, the home secretary was told by both Labour and SNP it would fall short because it would not have legal powers to compel witnesses to testify or disclose documents.

Couzens was known among former colleagues as The Rapist and he had exposed himself on two occasions.

Addressing the Conservative party conference, Patel said the killing “exposed unimaginable failures in policing”. She is yet to announce who will lead the non-statutory inquiry.

“It is abhorrent that a serving police officer was able to abuse his position of power, authority and trust to commit such a horrific crime. The public have a right to know what systematic failures enabled his continued employment as a police officer. We need answers as to why this was allowed to happen,” she said.

“I can confirm today that there will be an inquiry to give the independent oversight needed to ensure that something like this can never happen again.”

Nick Thomas-Symonds, the shadow home secretary, said: “Labour has been calling for a full independent inquiry for days. Now the home secretary has half-heartedly announced one, but not put it on a robust, statutory footing to ensure there are no barriers in the way to getting answers.”

The SNP’s justice and immigration secretary, Anne McLaughlin, said: “Right now it is not set to be a statutory inquiry, and there must be a statutory inquiry.”

A source close to Patel said that a statutory inquiry would give Couzens the opportunity to apply to be a core participant in the inquiry, which would be wholly inappropriate. “We will start the process as a non-statutory inquiry and see where it goes,” the source said.

In June, the chair of the inquiry into the unsolved murder of private investigator Daniel Morgan, Baroness O’Loan, said her inquiry was hampered and witnesses did not give evidence because it was not statutory.

“We could not compel witnesses to testify, nor could we compel the Metropolitan police to disclose documents in a timely manner,” she said.

The Labour peer Baroness Shami Chakrabarti has tabled an amendment to the police bill which would compel the home secretary to set up a statutory inquiry.

“If we needed a judicial inquiry for racism in 1997, we certainly need as much for misogyny in 2021,” she said.

The inquiry represents a change of direction for the government and will increase pressure on Cressida Dick, the Met police commissioner.

Boris Johnson said on BBC One’s Andrew Marr Show on Sunday that there was no need for an inquiry.

The culture of the Met has been under scrutiny since it emerged that Couzens was known by colleagues to have a history of sexual aggression towards women. He was known as The Rapist while working at the Civil Nuclear constabulary in Kent by colleagues, who also knew he liked rape pornography.

Questions have been raised about the Met’s vetting processes after it emerged Couzens was allowed to continue serving despite having been investigated by Kent police in 2015 for indecent exposure.

He used his warrant card and police-issued handcuffs to get Everard, 33, into a car before raping and strangling her and burning her body in woodland in Kent.

The first part of the inquiry would examine Couzens’ previous behaviour and establish a definitive account of his conduct leading up to his conviction, as well as any opportunities missed, drawing on the ongoing Independent Office for Police Conduct investigations, a Home Office statement said.

The second part will look at specific issues raised by the first part, which could include vetting practices, professional standards and discipline, and workplace behaviour.

Last week, it was revealed that five serving officers, including three from the Met, were under investigation for sharing racist and misogynistic messages with Couzens on a WhatsApp group.

A freedom of information request showed that more than half of Met officers found guilty of sexual misconduct over a four-year period to 2020 kept their jobs, a total of 43 officers out of 83.

Sadiq Khan, the mayor of London, wrote to Patel on Friday with a request to work together to hold Dick and her force to account and to restore public trust, his office said. They spoke again on Sunday evening after it emerged that another Metropolitan police officer, PC David Carrick, had been charged with rape.

Khan said the inquiry must address cultural issues within the force.

“All police officers must adhere to the highest possible standards; we must stamp out misogyny, sexism, racism and homophobia, root out those who abuse their trusted position as officers,” he said.

Patel also plans to write to the independent police inspectorate to commission a thematic inspection, including police forces’ ability to detect and deal with misogynistic and predatory behaviour. She has asked for initial findings by the end of 2021.

Dick, who was given a two-year extension to her contract last month, has rejected calls to resign over Everard’s murder. On Monday she ordered a review of the Met’s culture.

In a separate development, Johnson angered lawyers by claiming that the conduct of defence lawyers is responsible for the low level of rape convictions.

“The defence is too often able to produce a spurious or otherwise reason why the defendant might have thought consent was given,” he said on BBC Radio 4’s Today programme.

Jonathan Black, a former president of the London Criminal Courts Solicitors’ Association, wrote on Twitter: “Did I just hear @BorisJohnson on @BBCr4today blaming the delays in justice on defence seizing upon mobile phone evidence ? I flipping did.”