The Mayor of London wants a plan from the Metropolitan Police commissioner within weeks on how to "win back the trust and confidence" of the public.
Sadiq Khan met Dame Cressida Dick last week after the police watchdog found "disgraceful" misogyny, discrimination, bullying and sexual harassment among PCs based at Charing Cross.
His spokesperson said the commissioner had been "put on notice" as a result.
Mr Khan has now demanded a plan by the next time they meet.
Asked on BBC Radio 4's Today programme when that would be, the mayor said: "It's days and weeks."
And asked what he would do if he was unhappy with the response, Mr Khan added: "I won't keep silent about that, I'll take action."
Home Secretary Priti Patel said: "The public rightly expects the behaviour of the police to be beyond reproach - standards must be raised."
Dame Cressida, who has led the force since 2017, has come under increasing pressure over a string of issues within the force - including over the murder of Sarah Everard by a serving police officer.
The BBC's political editor, Laura Kuenssberg, said tensions arose between No 10 and the Home Office over the police chief's future in light of the horrific crime.
But it is understood that both Home Secretary Priti Patel and Prime Minister Boris Johnson were unenthusiastic about the likely internal candidate, senior Met officer Neil Basu, who had previously criticised the PM and was seen in No 10 as "too political".
As a result, Dame Cressida saw her term extended by a further two years until April 2024.
'I am not willing to wait'
Ms Patel - who is ultimately responsible for firing and hiring the force's commissioner - said it had been "clear for some time that there are problems with the culture of the Metropolitan Police".
She said she had launched an independent investigation into the "deeply concerning issues", and expected both the mayor and the force to implement any recommendations "as soon as practically possible".
Mr Khan said this could take months, adding: "We can't wait."
Speaking to Today, he said he wanted to hear the police chief's response to the revelations about police in Charing Cross at their next meeting.
But, more widely, he said he also wanted to see her plan "to win back the trust and confidence that's been both knocked and shattered as a consequence of these cases".
"We police in this country based on one important principle: consent," he added.
"If it is the case that Londoners, whether you are a woman or a girl, a person of colour or you are a member of the LGBT+ community, haven't got confidence in the police service to come forward when you are a victim of crime, to come forward when you are a witness of crime, to come forward and join the police service?
"That's a problem for now. I am not willing to wait."
He would not elaborate on what "action" he would take if he was unhappy with Dame Cressida's plan.
But the mayor added: "If there are examples of cultural practices or behaviour that is unacceptable, I have got to hold to account those who Londoners expect to be held to account."
Some MPs have defended Dame Cressida, with Tory Bob Blackman saying: "You cannot blame Cressida Dick for lunatics within the organisations who've let her down."
Labour MP Margaret Hodge also said the police chief was "really well liked by police officers" and she should be "given the opportunity to see if she can put this right".
Source: BBC News