The Home Secretary spoke with the under-fire Metropolitan Police Commissioner Dame Cressida Dick on Sunday, having received her report into the events on Saturday night.
But “in the interest of confidence in policing” Ms Patel asked Sir Thomas Winsor to conduct an independent review into what happened, a Government source told the PA news agency.
It came as Mr Khan said he would be asking HM Inspectorate of Constabulary and the Independent Office for Police Conduct to look into the events.
The mayor said the scenes at the vigil were “completely unacceptable” despite having received assurances from Scotland Yard last week that the vigil would be policed “sensitively”.
He 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.
“I will now be asking Her Majesty’s Inspectorate of Constabulary [HMIC] to conduct a full independent investigation of events yesterday evening and in previous days. I am also asking the Independent Office for Police Conduct [IOPC] 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.”
Dame Cressida is facing calls to resign after the clashes in which her force’s officers were seen grabbing several women and leading them away in handcuffs.
The Metropolitan Police later said four people were arrested for public order and coronavirus regulation breaches.
Liberal Democrat leader Sir Ed Davey called on Dame Cressida to resign, while Women’s Equality Party co-founder Catherine Mayer said her position was “untenable”.
Labour has not called for Dame Cressida to resign, with shadow domestic violence minister Jess Phillips saying: “The reality is if Cressida Dick stays or goes (it) doesn’t make women in this country more safe, and that’s what I want to talk about.”
She said there were “so many missed opportunities throughout the day for police to work with organisers to create a completely safe vigil so that people could go and have a moment of sorrow and a moment of resistance”.
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.
The woman, who has not yet been identified, then tries to bend down near the officers and is shoved back again. She can be heard shouting that she is trying to retrieve her glasses.
Reclaim These Streets had organised the vigil before being forced to cancel following consultation with the Metropolitan Police, which said it would be in breach in coronavirus restrictions.
It has asked Dame Cressida for an urgent meeting so she can “explain the actions taken by the police last night, before she reports to the Home Secretary”.
After the clashes, organiser Jamie Klingler said the force’s handling of events was a sign of the “systemic ignoring and oppressing of women”.
Hundreds of people converged on the south London park despite an official vigil being called off earlier in the day due to police warnings over coronavirus restrictions.
Vigils also took place in locations including Glasgow, Nottingham, Birmingham and Bristol.