London mayor Sadiq Khan has called for an independent investigation into the Metropolitan Police's actions at the vigil on Saturday.
He said that Commissioner Cressida Dick had failed to provide him with a satisfactory explanation.
Mr Khan said he would be asking HM Inspectorate of Constabulary and the Independent Office for Police Conduct to look into the event, after officers clashed with crowds who gathered to remember the 33-year-old on Clapham Common.
Officers from the Metropolitan Police were seen grabbing several women and leading them away in handcuffs.
The force later said four people were arrested for public order and coronavirus regulation breaches.
Mr Khan said the scenes at the vigil were "completely unacceptable", despite having received assurances from Scotland Yard last week that it would be policed "sensitively".
"In my view, this was not the case," he said.
Mr Khan said: "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.
"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," said Mr Khan.
People gathered in Clapham Common on Saturday to pay tribute to Sarah Everard who was found dead this week.
Ms Everard went missing while walking home from a friend's flat in south London on 3 March.
Her body was found hidden in an area of woodland in Ashford, Kent, on Wednesday.
Serving Metropolitan Police constable Wayne Couzens, 48, has been charged with kidnapping and killing the marketing executive.
In the early hours yesterday, Assistant Commissioner Helen Ball said police were put into a position "where enforcement action was necessary".
She said: "Hundreds of people were packed tightly together, posing a very real risk of easily transmitting Covid-19.
"Police must act for people's safety, this is the only responsible thing to do. The pandemic is not over and gatherings of people from right across London and beyond, are still not safe.
"Those who gathered were spoken to by officers on a number of occasions and over an extended period of time.
"We repeatedly encouraged those who were there to comply with the law and leave. Regrettably, a small minority of people began chanting at officers, pushing and throwing items."
The assembled crowd chanted "shame on you" as police led people away at the vigil, while during another confrontation a distressed woman could be heard telling officers "you're supposed to protect us".
In one video obtained by the PA news agency, a woman could be seen being shoved forcefully in the back by two officers after being lifted from her knees.
Vigils also took place in locations including Glasgow, Nottingham, Birmingham and Bristol.
