British Prime Minister Boris Johnson on Thursday expressed his shock at the discovery of human remains in a high-profile hunt for a missing woman that has seen a police officer arrested for murder.

The remains were found in woodland in Kent, southeast England, on Wednesday by detectives investigating Sarah Everard's disappearance.

The 33-year-old marketing executive has not been seen since she walked home from a friend's flat in south London on the evening of March 3.

Her disappearance has sparked renewed debate in Britain about women's safety in public spaces.

"I am shocked and deeply saddened by the developments in the Sarah Everard investigation," said Johnson.

"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."

His comments were echoed by interior minister Priti Patel who said her "heartfelt thoughts and prayers are with Sarah, her family and friends at this unbearable time".

Patel said the stories being shared online by women were "powerful because each and every woman can relate".

"Every woman should feel safe to walk on our streets without fear of harassment or violence," said Patel, whose brief includes crime and policing.

She said she would do all she could to "protect women and girls".

London's Metropolitan Police said on Wednesday a member of its elite diplomatic protection branch had been arrested on suspicion of murder.

The officer, who is in his 40s and whose name has not been released, was originally detained late on Tuesday on suspicion of kidnapping.

He is also being questioned on a separate allegation of indecent exposure.

A woman in her 30s was also arrested Tuesday on suspicion of assisting an offender.

Metropolitan Police Commissioner Cressida Dick has said confirming the identity of the remains may take "some considerable time".

Dick said the arrest of a police officer in the case had prompted "waves of shock and anger through the public and through the whole of the Met".

A "Reclaim These Streets" vigil will take place Saturday on Clapham Common, where it is believed Everard walked home.

Organisers of the event on social media have said: "In Clapham, police told women not to go out at night this week. Women are not the problem.

"This is a vigil for Sarah, but also for all women who feel unsafe," they added.

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