Commissioner Dame Cressida Dick is facing calls to resign after clashes between police and crowds who gathered on Clapham Common on Saturday night to remember the 33-year-old.
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.
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 demanded a full report on events – and described the scenes as “upsetting”.
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”.
Home Office minister Victoria Atkins said she took the events “very seriously” but that she wanted to give the commissioner “a chance to explain” what happened.
She told Sky’s Sophy Ridge On Sunday: “I really, really want to support the Home Secretary in her request to have a report from Cressida.
“The police have got a tough job in policing the coronavirus pandemic more generally at the moment.”
She added: “I think this morning given how difficult last night was, after what has been an incredibly upsetting week, I’m very keen that we don’t pre-empt that report and we give the Met Commissioner a chance to explain what happened last night.”
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 the early hours of Sunday, 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.
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.
After the clashes, organiser Jamie Klingler said the force’s handling of events was a sign of the “systemic ignoring and oppressing of women”.
“I think we were shocked and really, really sad and to see videos of policemen handling women at a vigil about violence against women by men… I think it was painful and pretty triggering to see,” Ms Klingler told the PA news agency the morning after officers were seen tussling with some of those in attendance.
“The fact that nobody stepped in and said: ‘Do you see how this looks?’ The fact that Thursday and Friday they wasted our organising time by dragging us to the High Court for our human rights to protest and we were going to have a silent vigil.
“Especially today, it’s Mother’s Day. It’s the week of International Women’s Day. And instead of allowing and facilitating it like the Lambeth police wanted to – and that police force was so supportive – Scotland Yard quashed us and in doing so silenced us and got the reaction they got last night.”
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.