The Metropolitan Police's handling of a vigil in south London to mourn Sarah Everard has been widely criticised across the political spectrum.
Home Secretary Priti Patel has asked the Met for a report on what happened, while London Mayor Sadiq Khan said he was "urgently seeking an explanation" from Commissioner Dame Cressida Dick.
Officers were seen handcuffing and leading women away from the event.
Police said four arrests were made at the vigil to "protect people's safety".
Several hundred people gathered on Clapham Common on Saturday evening to pay tribute to the 33-year-old - whose death has prompted a public debate over women's safety - despite Covid restrictions.
The official vigil, which was being organised by Reclaim These Streets, had been called off earlier in the day due to police warnings over coronavirus restrictions.
The group said they were "deeply saddened and angered" by the police's actions and criticised officers for "physically manhandling women at a vigil against male violence".
"It is their responsibility to protect public order, public health and the right to protest - they failed tonight on all accounts," the group added in a statement.
The Met said it was the "only responsible thing" for them to do to ensure public safety.
The force added that a review will be carried out to see if "lessons can be learned".
One video posted online showed officers removing women who were stood in the bandstand.
Cries of "shame on you" and "let them go" could be heard from onlookers. The video showed them being put in a police van and driven away.
Liberal Democrat leader Sir Ed Davey called for Commissioner Dame Cressida Dick to resign over the "utterly disgraceful" scenes.
Sir Ed said in a tweet that Dame Cressida had "lost the confidence of the millions of women in London".
Ms Patel called footage on social media "upsetting" and said she had asked the Metropolitan Police for a "full report on what happened".
Sadiq Khan, the Labour Mayor of London, said the scenes were "unacceptable" and that he was "urgently seeking an explanation" from the commissioner.
"The police have a responsibility to enforce Covid laws but from images I've seen it's clear the response was at times neither appropriate nor proportionate," he tweeted.
Labour leader Sir Keir Starmer said the scenes were "deeply disturbing".
"Women came together to mourn Sarah Everard - they should have been able to do so peacefully.
"I share their anger and upset at how this has been handled. This was not the way to police this protest," Sir Keir tweeted.
Conservative MP Caroline Nokes, who chairs the Commons Women and Equalities Select Committee, said she was "truly shocked" at the scenes on Clapham Common.
"In this country, we police by consent - not by trampling the tributes to a woman who was murdered and dragging other women to the ground. Badly misjudged by #metpolice," Ms Nokes tweeted.
Met Assistant Commissioner Helen Ball said hundreds of people were "packed tightly together", posing a risk of transmitting Covid-19.
"Police must act for people's safety, this is the only responsible thing to do," she said in a statement.
"We absolutely did not want to be in a position where enforcement action was necessary. But we were placed in this position because of the over-riding need to protect people's safety."
A tweet posted by Sisters Uncut alleged "male police officers waited for the sun to set before they started grabbing and manhandling women in the crowd".
Earlier, Reclaim These Streets said they had cancelled the official vigil because the Met Police had failed to "constructively engage" with plans to hold it in a Covid-secure way.
The group asked people not to gather at Clapham Common because it could put them "legally at risk".
Instead, it had urged mourners to light candles and shine other lights on their doorsteps at 21:30 GMT - to coincide with the time Ms Everard was last seen on 3 March.
Among those who took part in the doorstep vigil were Prime Minister Boris Johnson and his fiancée, Carrie Symonds, who lit a candle and placed it in front of No 10.
Earlier, Mr Johnson tweeted that he would "be thinking of her family and friends", adding: "I will do everything I can to make sure the streets are safe."
Scotland's First Minister Nicola Sturgeon tweeted a picture of a candle in her home, which she said was "for Sarah", while Wales's First Minister Mark Drakeford encouraged people to "ignite a fire for change".
The clashes occurred on Saturday evening, but people had visited the bandstand to lay flowers and pay their respects throughout the day.
The Duchess of Cambridge made a private visit on Saturday afternoon, and was seen pausing at the bandstand.
It is understood that she wanted to pay her respects to Ms Everard and her family.
Earlier on Saturday, Met Police officer Wayne Couzens, 48, appeared at Westminster Magistrates' Court charged with Ms Everard's kidnap and murder.
The 33-year-old disappeared when walking home to Brixton from Clapham in south London on 3 March.
Her body was found in an area of woodland in Ashford, Kent, Westminster Magistrates Court heard.
Mr Couzens was remanded in custody to appear again at the Old Bailey on 16 March.
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