While the event in Clapham, south London, was largely peaceful, scuffles broke out at the front of a crowd of hundreds as police surrounded a bandstand covered in floral tributes to the 33-year-old.
At one stage, male officers could be seen grabbing hold of several women before leading them away in handcuffs, to shouts and screams from onlookers.
In response, the crowd chanted “shame on you”, while during another confrontation a distressed woman could be heard telling officers “you’re supposed to protect us”.
The Home Secretary described footage of the clashes as “upsetting”, adding: “I have asked the Metropolitan Police for a full report on what happened.”
Mayor of London Sadiq Khan said the scenes were “unacceptable”, tweeting: “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.”
Mr Khan said that he was in contact with Met Commissioner Cressida Dick and was “urgently seeking an explanation”.
Labour leader Sir Keir Starmer described the scenes as “deeply disturbing”.
“Women came together to mourn Sarah Everard – they should have been able to do so peacefully,” he tweeted.
“I share their anger and upset at how this has been handled. This was not the way to police this protest.”
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.
While the Clapham clashes took place, many other peaceful vigils were held around the country in locations including Glasgow, Nottingham, Birmingham and Bristol – despite warnings over lockdown.
A virtual event was also held at 6pm in which campaigners called for more to be done to tackle violence against women.
Several female politicians expressed their anger at the Met over the officers’ tactics in Clapham.
Labour MP for Streatham Bell Ribeiro-Addy wrote on Twitter: “This could have been the socially distanced vigil the community needed to remember Sarah and all the women who have lost their lives to violence. We knew what was going to happen if the event was shut down.
She added: “I know Lambeth Borough officers made efforts to compromise with the organisers but were overruled from high up.
“They’ll be left to deal with the fallout of this and the further burden it places on already strained community relationships. Very disappointing from Scotland Yard.”
Campaign group Sisters Uncut, which had representatives present at the demonstration, claimed that “male police officers waited for the sun to set before they started grabbing and manhandling women in the crowd”.
Reclaim These Streets, which had planned to hold the Clapham vigil before it was cancelled, also urged people to take part in a doorstep vigil at 9.30pm on Saturday.
The group said it would be joining people across the country and “shining a light, a candle, a torch, a phone, to remember Sarah Everard and all the women affected by and lost to violence”.
They added: “We aren’t just lighting a candle for the women we’ve lost: we have been inspired by the women who have reached out and hope this is just the start of a movement that will light a fire for change.”
Prime Minister Boris Johnson said he would light a candle for Ms Everard with his fiancee Carrie Symonds, adding that he would be thinking of the 33-year-old’s family and friends.
“I cannot imagine how unbearable their pain and grief is. We must work fast to find all the answers to this horrifying crime,” he said.
“I will do everything I can to make sure the streets are safe and ensure women and girls do not face harassment or abuse.”
Home Secretary Priti Patel said she would also be lighting a candle, and added that almost 20,000 people had responded in 24 hours to a consultation on how the Government could tackle violence against women and girls.
Opening the online event alongside the campaign organisers, television presenter Sandi Toksvig said she had never “felt more passionately concerned about my kids”.
She said: “It surely cannot be asking too much to want them simply to be free, to walk where they like, when they like.”
She added that it was not a “small change” that was needed, but a “cultural shift about how women are viewed and treated both in the public and private space”.
“This has to be a turning point where ending violence finally becomes a political priority,” she said.
The Duchess of Cambridge was among those to visit the make-shift memorial at Clapham Common on Saturday to pay her respects, and was seen pausing in front of the sea of flowers.
Meanwhile, a fundraiser set up by Reclaim These Streets for women’s charitable causes passed its target of £320,000 on Saturday evening.
On Friday, a High Court judge refused to intervene on behalf of the group in a legal challenge over the right to gather for a protest during coronavirus restrictions.
On Saturday, the group said that despite their attempts to work with police to ensure the Clapham vigil could proceed safely, they now felt it could not go ahead.
Organisers said they had made “many suggestions” to police, including splitting the event into different time slots – but that they were told going ahead with a vigil could risk a £10,000 fine each for each woman organising.
Caitlin Prowle, from Reclaim These Streets, said the group had not wanted to end up in a situation they were having to raise funds to pay fines, rather than for charitable causes.
She said they had instead decided to raise money for charity as otherwise the fines would “just go straight back into a system” that “continues to fail” women.