There were a number of arrests after the police ordered the protesters to disperse, warning they were in breach of coronavirus regulations.
Ms Everard, 33, went missing while walking home in south London on March 3.
Ministers said they were committed to working with police forces and crime commissioners to ensure the measures were more focussed on preventing sexual violence.
Mr 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.”
A protest was held in London on Monday to campaign after the death of Ms Everard.
Demonstrators were told to go home or be arrested, as dozens were stopped over breaching Covid restrictions.
Another protestor was dragged through Tottenham Court Road by officers who pinned him up against a double-decker bus.
The ‘Kill the Bill’ demonstration snaked through Soho before heading south towards Elephant and Castle.
‘ACAB’ was scrawled on the side of a bus as activists made their way back across Vauxhall Bridge.
Crowds had gathered in the afternoon in nearby Parliament Square for a vigil in memory of Ms Everard, holding placards with slogans including “silence will not protect us” and “women matter”.
Chants of “sisters united will never be defeated” rang out and the crowd listened to speeches as dozens of police officers watched on.
Mr Johnson acknowledged that the scenes 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.
The Independent Office for Police Conduct (IOPC) said it had completed assessments of four referred cases and it would be commencing investigations into two of them.
Couzens sustained head injuries on March 10 and March 12 and was treated in hospital on both occasions.
The other investigation will examine an “inappropriate” graphic that was allegedly shared by an officer who took part in search operations.
The Met said the graphic was reported by a number of colleagues who were “concerned by its content”.