Cressida Dick is facing calls to quit her position as Met Police Commissioner to "rebuild the shattered confidence of women in the police service".
Labour MP Harriet Harman asked the Home Secretary to take urgent action after Met Officer Wayne Couzens was sentenced to life for the kidnap, rape and murder of Sarah Everard.
The MP for Camberwell and Peckham told the Met Police chief Commissioner she needed to step aside to "enable these changes to be taken through".
In a letter to Dame Cressida, Harriet Harman, who is also mother of the House of Commons said:
"Women need to be confident that the police are there to make them safe, not to put them at risk. Women need to be able to trust the police, not to fear them.
"I have written to the Home Secretary to set out a number of actions which must be taken to rebuild the shattered confidence of women in the police service.
"I think it is not possible for you to lead these necessary actions in the Metropolitan Police. I am sure that you must recognise this, and I ask you to resign to enable these changes to be taken through and for women to be able to have justified confidence in the police."
In a second letter to Home Secretary Priti Patel discussing the crimes of Wayne Couzens, she said: "It is clear that there had been all too many warning signs about him which had been swept under the carpet. It cannot be rebuilt with the attempt to reassure that this was just, as the Metropolitan Police Commissioner said, one 'bad'un'.
"Women's confidence in the police can only be rebuilt with substantive and immediate change."
She called on the Home Secretary to bring forward changes including:
Immediately suspending officers from duty where there is an allegation of violence against women
Dismissing officers immediately when there is a conviction or admission of such a crime
Disciplinary action of gross misconduct, leading to dismissal, for failing to report fellow officers for an allegation of violence against women
Scrutinising someone's attitudes to violence against women, including engaging in violence during sex, as part of vetting of police recruits
Fresh checks on officers who transfer between forces for allegations of violence against women
Training for all current serving officers with a course to teach them to "examine their own attitudes to violence against women and recognise signs in their colleagues"
Responding to the whole life sentence given to Wayne Couzens Priti Patel said: “What we heard today is sickening to everyone and there are no words, no words at all, that can describe the appalling tragedy around Sarah Everard’s murder.
“All our thoughts and our sympathy are with her family and she is constantly in my thoughts as well.
“In terms of the monster that has been convicted today, it is right that he has been given a whole life tariff and with that he can never walk the streets of our country again.
“Alongside that of course, it is right that we constantly hold the police to account for what has happened.”
Earlier this year, Dame Cressida said "what happened to Sarah appals me" but it has made her "more determined, not less, to lead my organisation."
She said that "all the women and men of the Met are outraged at what has happened."