The discovery was made in an area of woodland in Ashford in Kent, Commissioner Cressida Dick said on Wednesday evening.
“We are not able to confirm any identity. That may take some considerable time,” she added.
Ms Everard, 33, disappeared last Wednesday as she walked home from a friend’s house in Clapham, south London.
A serving Metropolitan Police officer who works in the Diplomatic Protection Command in Westminster has been arrested on suspicion of murdering Ms Everard.
The officer was initially arrested on suspicion of kidnapping her, but on Wednesday, Scotland Yard said the man in custody had further been arrested on suspicion of murder.
It is understood the officer had not been on duty when Ms Everard disappeared.
He has also been arrested on suspicion of a separate allegation of indecent exposure.
Ms Everard’s disappearance in “awful and wicked circumstances” are every family’s nightmare, Ms Dick said.
She said Londoners should know that it is “thankfully incredibly rare” for a woman to be abducted from the capital’s streets and said her thoughts are with Ms Everard’s family.
Ms Dick added: “The news today that it was a Metropolitan Police officer who was arrested on suspicion of Sarah’s murder has sent shockwaves and anger through the public and through the Met.
“I speak on behalf of all my colleagues when I say that we are utterly appalled at this dreadful, dreadful news.
“Our job is to patrol the streets and to protect people.”
More as we have it.