A body found by police in woodland on Wednesday has been confirmed as that of Sarah Everard.
The 33-year-old marketing executive disappeared as she walked home in south London last week.
A serving Met Police officer remains in custody having been held on suspicion of Ms Everard's kidnap and murder.
In another development, organisers of a vigil for Ms Everard lost a legal challenge at the High Court against a police ban on the event.
Organisers claimed there had been an "about-face" by police, who told them that Saturday's Reclaim These Streets event in Clapham would not now be permitted due to the coronavirus lockdown, having previously said the gathering could go ahead.
Ms Everard was last seen on 3 March walking alone down a main road in Clapham at 21:30 GMT, with police saying it was unclear whether she reached her home in Brixton.
On Friday evening, Met Police Commissioner Dame Cressida Dick took part in a walkabout on Clapham Common.
She walked with police officers and spoke to members of the public in the park close to Clapham Common Tube station.
Earlier, speaking outside New Scotland Yard, Assistant Commissioner Nick Ephgrave gave a televised update on the police inquiry.
"As you know, on Wednesday evening detectives investigating the disappearance of Sarah Everard discovered a body secreted in woodland in Kent," he said.
"The body has now been recovered and formal identification procedure has now been undertaken."
He said specialist officers remained in constant contact with Ms Everard's family and that hundreds of officers were working "round the clock" to establish the full circumstances of her disappearance.
"I know that the public feel deeply hurt and angry and I speak on behalf of all my colleagues when I say that we too are horrified," he said.
Throughout the week, searches have been carried out in Clapham, where Ms Everard was last seen, as well as at a home in Deal and the woodland in Ashford.
On Tuesday, the Met officer was arrested in Kent on suspicion of Ms Everard's kidnap and was later rearrested on suspicion of her murder.
The man, who is in his 40s and works with the Met's Parliamentary and Diplomatic Protection Command, was taken to hospital on Thursday suffering from head injuries he sustained while alone in his cell.
He was treated, discharged and returned to the police station where he is being held, after an application to extend his detention was granted by magistrates.
A woman in her 30s, who was arrested on suspicion of assisting an offender, has been released on bail until mid-April.
The Met is facing an investigation by the police watchdog into its handling of a separate allegation of indecent exposure against the arrested officer.
The Independent Office for Police Conduct (IOPC) is to look at whether officers "responded appropriately", after the Met received two complaints that a man had exposed himself at a fast food restaurant in south London on February 28 - three days before Ms Everard went missing.
- 3 March: Sarah Everard vanishes after leaving a friend's house on Leathwaite Road, Battersea, about 21:00 GMT
- 5 March: Police say they are "increasingly concerned" for Ms Everard and make an appeal on Twitter
- 6 March: Ms Everard's family, who are from York, say her disappearance is "totally out of character" as officers search Clapham Common's ponds
- 7 March: Footage taken from a doorbell camera shows Ms Everard walking alone along the A205 Poynder Road towards Tulse Hill at 21:30. Police say it is unclear whether or not she reached her house in Brixton
- 8 March: More than 120 calls are made from the public on the case and more than 750 homes are visited as part of the investigation
- 9 March: A serving officer is arrested in Kent along with a woman who is held on suspicion of assisting an offender
- 10 March: Met Police Assistant Commissioner Nick Ephgrave describes the arrest as "shocking and deeply disturbing". Extensive searches are carried out in parts of Kent. Later in the evening Commissioner Dame Cressida Dick said human remains had been found in woodland in Kent
- 11 March: Suspect taken to hospital after suffering head injuries while in custody. The woman arrested on suspicion of assisting an offender is released on bail
- 12 March: Body found in Kent woodland confirmed to be that of Ms Everard