The new Metropolitan Commissioner must tackle policing culture and conduct, the home secretary has said.
Writing in the Evening Standard, Priti Patel said “strong and decisive new leadership will be required to restore public confidence”.
Dame Cressida said she had been left with “no choice” but to resign, after London’s mayor made it clear to her he had no confidence in her leadership.
It follows cases of sexism and misogyny among some Met officers.
Last week, the police watchdog found “disgraceful” examples of bullying and sexual harassment at Charing Cross police station.
Dame Cressida, the first woman to lead the biggest UK police force, also faced criticism over the murder of Sarah Everard by a serving Met officer last year, and a series of other scandals.
Beyond London, the Met is also responsible for national counter-terrorism policing, and Ms Patel said the Met commissioner “is a national leader, with a critical national role”.
The BBC has been told the home secretary has clashed with the Labour mayor over the resignation.
Home Office sources said they were “astounded” that Mr Khan’s previous comment that Dame Cressida had “days and weeks” to sort out the Met turned into “less than 48 hours”.
Dame Cressida is thought to have offered her resignation after declining to meet Mr Khan to discuss her plans for reforming the Met – but the BBC understands he did not inform Priti Patel about the meeting.
Dame Cressida’s successor will be appointed by the home secretary, in consultation with the mayor of London. Contenders include Matt Jukes and Neil Basu, who are both assistant Met commissioners.
Dame Cressida said she had “agreed to stay for a short period to ensure the stability of the Met”.
Former Met Police commissioner Sir Paul Stephenson told LBC “we should be casting the net as wide as possible” to find the best candidate for the role, including outside policing.
Ms Patel said the new commissioner must be “focused on the basics”, including tackling the abuse of women and girls, drugs and knife crime.
“Policing culture and conduct have rightly come under scrutiny,” she added. “Be in no doubt that a new leader must tackle these institutional issues.”
Speaking on BBC London hours before her departure was announced, Dame Cressida insisted that she had “absolutely no intention” of quitting, and that she was “seething angry” about the culture at Charing Cross, which was exposed by the police watchdog.
But Mr Khan said he was “not satisfied” with Dame Cressida’s response to the scale of change required to “root out” racism, sexism, homophobia, bullying and misogyny in the Met.
“On being informed of this, Dame Cressida Dick has said she will be standing aside,” he said.
The Met had submitted a plan to Mr Khan last Friday on reforming the force and a meeting was due to be held on Thursday afternoon.
A City Hall source said Mr Khan made it clear through his officials – but not directly to the commissioner – that the plan was not going to work and the meeting was cancelled.
Susan Hall, leader of the Greater London Assembly Conservatives, said Mr Khan had handled the situation “extremely badly”.
She said the resignation made Londoners less safe and left a “void” at the top of the Met.
A decision taken for her
Analysis by Tom Symonds, home affairs correspondent
On Thursday morning she was adamant. She wasn’t going. But all the signs are that the decision was taken for her by Sadiq Khan.
The commissioner of the Metropolitan Police is appointed by the Queen, on the advice of the home secretary, but the commissioner cannot do the job without the support of the mayor.
In the last few weeks attempts were made to convince him that the Met’s plan would deliver change.
But that plan involved a review – by Dame Louise Casey – that would have taken much of the year.
She had been given the power to roam freely through the force looking for bad attitudes and poor management of disciplinary issues.
That would have been a period when more revelations were inevitably going to emerge making the commissioner’s position even more difficult.
The mayor’s timetable was different – days, weeks at most. He needed to be convinced. His officials didn’t sound it on Wednesday. Thursday night’s development is the result.
Dame Cressida, who served in the role for almost five years and was recently given a two-year contract extension, said in a statement: “The murder of Sarah Everard and many other awful cases recently have, I know, damaged confidence in this fantastic police service.”
She added: “There is much to do – and I know that the Met has turned its full attention to rebuilding public trust and confidence.”
Harvey Proctor, a former MP falsely accused of murder during a disastrous probe into claims of a VIP paedophile ring, said her departure had come not a “day too soon” and called for a full inquiry into all her “personal mistakes”.
The partner of a man who was murdered by serial killer Stephen Port said the resignation was “about time” and that Dame Cressida was not capable of dealing with the homophobia, sexism and racism within the Met.
Ricky Waumsley previously called for her to quit after an inquest jury found police failures had likely contributed to the death of his partner Daniel Whitworth and two more of Port’s victims.
Prime Minister Boris Johnson said Dame Cressida “has served her country with great dedication and distinction over many decades”.
Shadow home secretary Yvette Cooper thanked Dame Cressida for her public service and said reform was needed to rebuild public confidence after recent cases.
Lib Dem leader Sir Ed Davey said a change in the force’s leadership was “long overdue”.
He added that Mr Johnson, whose part in the Downing Street parties held during lockdown is still being investigated by the Met, must have no role in choosing her successor.
But Ken Marsh, the chairman of the Metropolitan Police Federation, which represents rank and file officers in London, said Dame Cressida had been unfairly treated and the association had believed “she was the person who could take us through this”.
Controversies of Cressida Dick’s career
- Officers based at Charing Cross police station were found by an inquiry to have joked about rape and exchanged offensive social media messages. The Met said it was “deeply sorry”
- The delay to the publication of Sue Gray’s full report into lockdown parties at Downing Street was a “stitch-up” between the Met and No 10, the SNP and Liberal Democrats said. The Met’s investigation is ongoing
- The rape, abduction and murder of Sarah Everard by a serving Met Police officer prompted a wave of criticism and scrutiny
- Further controversy came when clashes broke out between women and police officers at a vigil in her memory, held under Covid lockdown measures
- There was condemnation of how police handled the murder of two women, Nicole Smallman and Bibaa Henry, in a park in Wembley. Two constables were jailed for sharing photos of the murdered sisters’ bodies and their mother said their disappearance would have been dealt with more urgently if they were white
- Dame Cressida also had to deal with the repercussions from the disastrous Operation Midland, the multimillion-pound investigation which saw detectives duped by false claims of a VIP sex abuse ring made by the paedophile and fantasist Carl Beech
- A report by an independent panel set up in 2013 into the unsolved murder of Daniel Morgan accused the force of institutional corruption, and found that the then-Assistant Commissioner Dame Cressida had initially refused to grant access to a police internal data system
- Before she became commissioner, she was in charge of the operation that led to the fatal shooting of Jean Charles de Menezes by officers who mistook him for a suicide bomber