The Mayor of London added he was “not satisfied” with the explanation he had been given by the force’s leadership after officers were seen grabbing several women and leading them away in handcuffs.
Commissioner Dame Cressida Dick has been facing calls to resign after clashes between police and crowds who gathered on Clapham Common night to remember the 33-year-old.
The force later said four people were arrested for public order and coronavirus regulation breaches.
But there has been condemnation of the policing of the vigil, which centred around a bandstand covered in flowers left in tribute.
Home secretary Priti Patel has asked Sir Thomas Winsor, Chief Inspector of Constabulary, to conduct a “lessons learned” review into the policing of the vigil, a government source told the PA news agency.
Khan said: “The scenes arising from the policing of the vigil for Sarah Everard held on Clapham Common last night were completely unacceptable. My thoughts remain with Sarah’s family at this awful time.
“I can completely understand why women, girls and allies wanted to hold a vigil to remember Sarah and all women who have been subjected to violence or lost their lives at the hands of men, and to reclaim the public spaces where women are made to feel so unsafe.
“Last week I called on the government and police to work with the organisers of the vigil to clarify the law and find a way for it to take place legally and safely. On Friday a High Court judge made clear there was a window to agree a way for a vigil to go ahead safely.
“I received assurances from the Metropolitan Police last week that the vigil would be policed sensitively. In my view, this was not the case.
“I asked the Commissioner and Deputy Commissioner to come into City Hall today to give me an explanation of yesterday’s events and the days leading up to them. I am not satisfied with the explanation they have provided.
“I will now be asking Her Majesty’s Inspectorate of Constabulary to conduct a full independent investigation of events yesterday evening and in previous days. I am also asking the Independent Office for Police Conduct to investigate the actions of police officers yesterday evening.
“It is vital that these events are not allowed to undermine the powerful calls since Sarah’s murder for meaningful action to finally stop men inflicting violence on women. It was clear before yesterday that there isn’t adequate trust and confidence from women and girls in the police and criminal justice system more widely. Further steps must now be taken to address this.”