A senior MP has led calls for the Met Police commissioner to resign, after the man who murdered Sarah Everard while he was a serving officer was sentenced to a whole-life prison term.
Labour MP Harriet Harman told Dame Cressida Dick women's confidence in the police "will have been shattered".
In her letter she wrote it would not be possible for Dame Cressida to oversee the changes needed to rebuild trust.
But the home secretary said she would "continue to work with" Dame Cressida.
Priti Patel added she would continue to hold the Met and Dame Cressida to account "as everybody would expect me to do".
Wayne Couzens, 48, kidnapped, raped and murdered Ms Everard, 33, in March.
The Old Bailey heard how Couzens used his Metropolitan Police warrant card and handcuffs to abduct Ms Everard under the guise of an arrest, as she was walking home from a friend's house in Clapham, south London.
At the time of the murder, Couzens was a serving firearms officer for the Parliamentary and Diplomatic Protection Command, working at diplomatic premises around central London.
He was sacked by the Met after pleading guilty.
Ms Harman, chairwoman of the Joint Committee on Human Rights and a former justice minister, is a prominent campaigner on women's rights.
She has also written to Home Secretary Priti Patel, calling for urgent changes to rebuild women's confidence in the police.
Her proposals include tougher action against officers accused of violence against women and stricter vetting of recruits.
In her letter to Dame Cressida, Ms Harman, who is also Mother of the House - the longest continuously serving female MP - wrote: "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."
"Women need to be confident that the police are there to make them safe, not to put them at risk," she added.
"Women need to be able to trust the police, not to fear them."
Ms Harman told Ms Patel "too many warning signs" about Couzens "had been swept under the carpet" and women's confidence in the police "cannot be rebuilt with the attempt to reassure that this was just, as the Metropolitan Police commissioner said, one 'bad'un'."
A former Met chief superintendent also said Dame Cressida should quit.
Parm Sandhu told BBC Radio 4's World at One programme a "complete overhaul" of vetting procedures was needed and she did not have trust in the Met commissioner to make the necessary changes.
"I think she has done as good a job as she can, she cannot move with the times and she needs to go," she added.
Zoe Billingham, who is standing down after 12 years in her role at Her Majesty's Inspector of Constabulary, described the case as "a watershed moment for policing", saying Couzens' crimes had "struck a hammer blow to policing legitimacy in England and Wales".
"We cannot abide by the narrative that this was a one-off and I think every force now in the country must look to re-establish trust and legitimacy," she told BBC Radio 4's Woman's Hour.
"I'd call on every force to now account immediately - not tomorrow, today - to its communities - as to exactly what it's going to do to ensure that this can never happen again."
But her boss Sir Thomas Winsor, Her Majesty's Chief Inspector of Constabulary for England and Wales, told BBC Radio 4's World at One that Dame Cressida should not go.
"Cressida Dick is not responsible for the individual acts of every police officer, including a police officer of the appalling criminal proclivities and intent of Wayne Couzens.
"Cressida Dick has a great deal of support from her officers and has led the Metropolitan Police with distinction. Not everything in the Met is good and we have published many reports that are critical of the Met, but this is not a case for the resignation of the commissioner."
Dame Cressida became the first woman to lead London's force when she was appointed in 2017.
Earlier this month, it was announced that she will serve an extra two years in her role and remain in post until 2024.