The Mayor of London, Sadiq Khan, said: "I can only imagine the pain and terrible agonies that Sarah Everard's family and friends are going through right now. My thoughts and prayers are with them.
"I am in regular contact with the Met Police Commissioner about the continuing investigation into Sarah's disappearance. A serving Met officer has been arrested on suspicion of murder.
“All women and girls should be able to feel safe on the streets of London at all times, and I know how shocked and worried Londoners are by Sarah’s disappearance and the developments in the case.
“I want to assure Sarah’s family, and everyone in our city, that the police are doing absolutely everything they can to find her.
“Londoners will continue to see more police officers on our streets continuing their investigation and carrying out reassurance patrols in the area where Sarah went missing a week ago.
“I know how concerned the public will be at the news that a serving police officer has been arrested, and it is right that the case has been referred to the police watchdog for independent investigation.
“I urge anyone with any information at all, even if you think it is small or insignificant, to come forward and call the Met’s Incident Room on 0208 785 8244, or by calling Crimestoppers, anonymously, on 0800 555 111.”