Plainclothes police officers in London will video call a uniformed colleague to confirm their identity when stopping a lone woman, the head of the Metropolitan police has announced in the wake of Sarah Everard’s abduction and murder.

Cressida Dick said the change would put the responsibility on the officer to prove they were acting properly, after senior police figures were criticised for their reaction to the case in which a serving officer, Wayne Couzens, was jailed for life for staging a fake arrest before kidnapping and burning Everard’s body in March.

When Couzens’ sentence was handed down last month, Scotland Yard suggested people stopped by a lone plainclothes officer should challenge their legitimacy or run away and wave down a bus to escape someone they thought might be pretending to work for the police.

A police and crime commissioner in North Yorkshire, Philip Allott, was forced to resign after he said women should educate themselves about “when they can be arrested and when they can’t be arrested”.

Dick said a new instruction had been issued that “allows a woman who is stopped by such a police officer immediately to have verification that this is a police officer”. The officer would make a video call to a sergeant in uniform “who will say: ‘yes that’s so-and-so, he’s PC XYZ,'” she explained.

The Met commissioner said it would be “a quick and easy way” women could regain confidence they were being stopped by a police officer acting properly, and added this would be “instigated by the officer, not by the woman having to ask for this”.

Dick, who last month got a two-year extension to her post as the most senior police figure in the country, added: “I want to be clear, the onus is on the officer … to deal professionally with the person that they are speaking to, and in the very unusual circumstance in which a plainclothes officer is talking to a lone female, which is likely to be extremely unusual in London, we would expect them to go to every effort first of all to recognise that the woman may feel uncomfortable, to explain themselves well, to identify themselves well.

“It would normally be the case that they would be in a pair anyway.”

Wiltshire police have already announced a similar scheme whereby officers will put their personal radio on loudspeaker and ask their control room to confirm their identity.

Kit Malthouse, the policing minister, also announced on Wednesday that an independent inquiry launched in the wake of Everard’s murder could be given greater powers if its chair feels people are not cooperating with it.

Shadow Home Office minister Sarah Jones said it should be put on a statutory footing to ensure the review could compel witnesses to testify and demand documents to help “rebuild the trust and confidence” of women and girls in the police.

Malthouse told MPs this would be a “very long-winded affair to set up” and a non-statutory inquiry would be “much quicker” – but added if the chair of the inquiry felt they needed it to be be made statutory, “we reserve the right to convert” it.

He added Everard’s murder “shook our country to the core” and that a chair of the forthcoming inquiry would be appointed shortly, with the terms of reference following after. A taskforce is also being launched “to drive cross-government action to maintain public confidence in policing”.