Dubbed ‘Project Vigilant’, the programme can involve officers attending areas around clubs and bars undercover, along with increased police patrols as people leave at closing time.
It also said ministers were committed to working with police forces and with police and crime commissioners to ensure the measures were more focused on preventing sexual violence.
Hundreds gather in Parliament Square for Sarah Everard vigil as MPs debate policing bill
Boris Johnson said it could mean siting measures in parks and routes used by women on their walks home.
“The horrific case of Sarah Everard has unleashed a wave of feeling about women not feeling safe at night. We must do everything we can to ensure our streets are safe,” he said.
“Ultimately, we must drive out violence against women and girls and make every part of the criminal justice system work to better protect and defend them.”
There were a number of arrests after the police ordered the protesters to disperse, warning they were in breach of coronavirus regulations.
Serving Metropolitan Police officer Wayne Couzens, 48, has been charged with her kidnapping and murder.
Mr Johnson acknowledged that the scenes – when a number of women were arrested – had been “distressing” but said the police had a “very, very difficult job” to do.
He said that Sir Thomas Winsor, chief inspector of constabulary, would be carrying out a review into the way the event was policed.
“I think people have got to have confidence in the police and Tom’s going to look at that,” he said.
Earlier in a Commons statement, Home Secretary Priti Patel said “too many” women felt unsafe in public.
“Too many of us have walked home from school or work alone, only to hear footsteps uncomfortably close behind us,” she said.
“Too many of us have pretended to be on the phone to a friend to scare someone off.
“Too many of us have clutched our keys in our fist in case we need to defend ourselves and that is not OK.”
She said footage of the Clapham Common event – where four protestors – were arrested had been “upsetting”.
But she defended restrictions on protests put in place to curb the spread of coronavirus, urging people not to participate in large gatherings while they remained in force.
“The right to protest is the cornerstone of our democracy, but the Government’s duty remains to prevent more lives being lost during this pandemic,” she said.
The Clapham Common vigil had originally been organised by the protest group Reclaim These Streets before it was forced to cancel after police said it would be in breach of coronavirus rules.
An organiser from the group said on Monday she did not want Dame Cressida to resign, but asked for the police chief to meet with them.
Anna Birley told ITV’s Good Morning Britain: “We are a movement of women seeking to support and empower other women, and as one of the most senior women in British policing history, we do not want to add to the pile-on.”
Hundreds of women have left floral tributes in the park near to the route where Ms Everard, who went missing while walking home from a friend’s flat on March 3, walked.
Throughout Monday, mourners arrived from across the capital to leave flowers and cards on the bandstand at Clapham Common.