The Metropolitan Police said on Wednesday night that remains had been found in an area of woodland in Ashford in Kent by detectives investigating the disappearance of the 33-year-old, who is originally from York.
A serving police officer in the Parliamentary and Diplomatic Protection Command had earlier been arrested on suspicion of Ms Everard’s kidnap and murder.
Met Commissioner Cressida Dick sought to reassure the public in the wake of Wednesday’s developments, saying “it is thankfully incredibly rare for a woman to be abducted from our streets”.
She added: “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.”
Boris Johnson said: “I am shocked and deeply saddened by the developments in the Sarah Everard investigation. Like the whole country, my thoughts are with her family and friends. We must work fast to find all the answers to this horrifying crime.”
The Met said the arrested officer’s main job was uniformed patrol of diplomatic premises, but would not specify where he had worked. He was not on duty at the time of Ms Everard’s disappearance.
The diplomatic protection squad is responsible for guarding the Parliamentary estate including Downing Street and the Palace of Westminster, as well as embassies in London.
The officer, in his 40s, was also arrested over a separate allegation of indecent exposure, the Met said.
A woman in her 30s has been arrested on suspicion of assisting an offender.
In a statement, Ms Dick said: “The news today that it was a Metropolitan Police officer arrested on suspicion of Sarah’s 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. Our job is to patrol the streets and to protect people.”
Investigators are continuing to work “around the clock” on what Ms Dick described as a “very fast moving” case.
The remains have not yet been identified and it could take some time to do so, the Commissioner added.
She said people living around Clapham and Tulse Hill could expect to see increased patrols in the area. As well as the search of the woodland in Ashford, over the course of Wednesday, officers also searched a property in Deal, Kent.
Multiple cars were taken away by investigators and a neighbour said a police officer lived at the address with his wife and two children.
Marketing executive Ms Everard vanished while walking home from a friend’s flat in south London on Wednesday March 3. Ms Everard is thought to have walked through Clapham Common towards her house in Brixton – a journey which should have taken around 50 minutes.
She was last captured on a doorbell camera walking along the A205 Poynders Road towards Tulse Hill at around 9.30pm on March 3.
A vigil titled “Reclaim these streets” has been organised on Facebook and is due to take place at Clapham Common bandstand at 6pm on Saturday evening.
Organisers said: “It’s wrong that the response to violence against women requires women to behave differently. In Clapham, police told women not to go out at night this week. Women are not the problem.
“We’ve all been following the tragic case of Sarah Everard over the last week. This is a vigil for Sarah, but also for all women who feel unsafe, who go missing from our streets and who face violence every day.”