Human remains have been found in the search for missing Sarah Everard, Met Commissioner Cressida Dick has said.
Ms Everard, 33, was last seen on 3 March in Clapham, south London, on her way home from a friend's house.
Detectives have not yet been able to confirm the identity of the remains, which were discovered in woodland near Ashford, Kent.
The officer, who has not been named by police, was arrested in Kent and is also being questioned about a separate allegation of indecent exposure.
Ms Everard, a marketing executive, was last seen in doorbell video footage walking alone down a main road near Clapham at 21:30 GMT, with police saying it was unclear if she reached her home in Brixton.
In a televised statement, Dame Cressida confirmed officers searching an area near Ashford had "found, very sadly, what appears to be human remains".
The Met Police commissioner said specialist officers had updated Ms Everard's family on the investigation.
Dame Cressida continued: "Sarah's disappearance in these awful and wicked circumstances is every family's worst nightmare.
"I know Londoners will want to know that it is thankfully incredibly rare for a woman to be abducted from our streets.
"But I completely understand that despite this, women in London and the wider public - particularly those in the area where Sarah went missing - will be worried and may well be feeling scared."
Dame Cressida said the arrest of a serving Met Police officer on suspicion of murder "has sent waves of shock and anger through the public and through the whole of the Met".
"I speak on behalf of all my colleagues in the Met when I say we are utterly appalled at this dreadful news," she added. "Our job is to patrol the streets and to protect people."
Hundreds of officers have been drafted in to help with the investigation as searches continue in south London and Kent.
The arrested officer was responsible for uniformed patrolling of diplomatic premises - including Downing Street and the Palace of Westminster, as well as foreign embassies in London.
He was off duty at the time of Ms Everard's disappearance.
A woman in her 30s was also arrested in Kent on Tuesday evening on suspicion of assisting an offender.
Prime Minister Boris Johnson said his thoughts were with Ms Everard and her friends and family.
The former Durham University student, who is originally from York, was last seen wearing a green rain jacket, navy blue trousers with a white diamond pattern, and turquoise and orange trainers.
She is also thought to have been wearing green earphones and a white beanie hat.
The case has been referred to the Independent Office for Police Conduct (IOPC) because it involves a police officer.
A spokesman said it had been decided that the Met Police would investigate any potential conduct issues linked to the kidnap and murder allegations itself.
The IOPC is currently assessing whether any further measures should be taken in relation to the actions of police after Ms Everard was reported missing.
The BBC's home affairs correspondent Daniel Sandford said that if it did turn out that a Met Police officer had been involved then there would be a "very strong sense of betrayal from the very top of [the organisation] down to the rank and file".
He said the force would also feel the people of London "above all" will have been betrayed "because they feel a deep sense of pride that their job is to protect the people of London and now here is one of their own officers suspected of doing the exact opposite in the worst possible way".
- 3 March: Sarah Everard vanishes after leaving a friend's house on Leathwaite Road, Battersea, about 21:00 GMT
- 5 March: Met Police are "increasingly concerned" for Ms Everard and make an appeal on Twitter
- 6 March: Ms Everard's family 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 have been found in a woodland in Kent