Met Police officer Wayne Couzens has pleaded guilty to the murder of Sarah Everard.
The firearms officer snatched her as she walked home from a friend's house in Clapham on 3 March, driving her away in a car he had hired.
The 33-year-old's body was found a week later in woodland near Ashford, Kent, metres from land owned by Couzens. She had been raped and strangled.
Couzens, 48, will be sentenced at the Old Bailey on 29 September.
Met Commissioner Dame Cressida Dick was in court when Couzens pleaded guilty.
Speaking outside the Old Bailey, Dame Cressida said she felt "sickened, angered and devastated" by his crimes.
She added: "They are dreadful and everyone in policing feels betrayed.
"Sarah was a fantastic, talented young woman with her whole life ahead of her and that has been snatched away."
The Independent Office for Police Conduct said on Friday that a total of 12 gross misconduct or misconduct notices had so far been served on police officers from multiple forces in relation to the Couzens case, including about the handling of two separate claims that Couzens had indecently exposed himself.
Prosecutor Tom Little QC told the court that Couzens and marketing executive Ms Everard had been "total strangers to each other".
On the night Ms Everard was snatched, she and Couzens were seen on camera standing by his hire car.
It was parked on the pavement with its hazard lights flashing.
Couzens drove them out of London to Tilmanstone, near Deal in Kent. Investigators were able to track the route he took using CCTV and identified the driver through the car hire firm.
The police constable had made the booking in his own name, picking up the Vauxhall Astra on the afternoon of the abduction and returning it the next morning. He was arrested on 9 March, only minutes after he had wiped the data from his mobile phone.
In Court 12 of the Old Bailey five members of Sarah Everard's family sat listening as police officer Wayne Couzens pleaded guilty to her murder.
On video-link from Belmarsh Prison he kept his head down and was shaking slightly.
As the barrister representing Couzens said his guilty plea was a sign of his remorse and the burden he would have to bear, Sarah's mother raised her hands.
It seemed as if she was saying that wasn't much comfort now.
The Met Police Commissioner Cressida Dick was also in court. Her force caught the murderer, only to discover it was one of her own officers.
Questions remain for the Met Police.
In his police interview, Couzens said he had got into trouble with a gang of Eastern Europeans who threatened him and his family.
They demanded he deliver "another girl" after he had underpaid a prostitute a few weeks before, the firearms officer said.
He claimed he kidnapped Ms Everard, drove out of London and handed her over to three men in a van in a layby in Kent, while she was alive and uninjured.
Meanwhile, police found out that Couzens and his wife owned a small patch of woodland in Ashford.
Phone data led officers to the site and Ms Everard's body was found just outside the property boundary the day after Couzens' arrest.
On Friday, Couzens' defence barrister told the court his client's admission of murder "represents a truly guilty plea and remorse for what he did and, as he put it to us this morning, he will bear the burden for the rest of his life - his words - 'as I deserve'."
Judge Lord Justice Fulford - who before adjourning the case discussed legal precedents for whole-life prison sentences - told the court: "This has been a mammoth investigation which has produced some very significant results in terms of being able to understand what happened."
Speaking after the conviction, the Crown Prosecution Service's Carolyn Oakley said: "Wayne Couzens lied to the police when he was arrested and to date, he has refused to comment.
"We still do not know what drove him to commit this appalling crime against a stranger.
"Today is a day to remember Sarah and our thoughts remain with her family and friends."