Investigators continue to question a serving Metropolitan Police officer, who was arrested on suspicion of murder, as human remains were found in the search for Sarah Everard.
The 33-year-old marking executive disappeared while walking home from Clapham to Brixton, south London, on the evening of 3 March.
The Met said on Wednesday night that the remains, which have not yet been formally identified, were found in an area of woodland in Ashford, Kent.
Officers have also searched a house in Deal, Kent, said by neighbours to belong to an officer and his wife.
The arrested officer, who is part of the force's Parliamentary and Diplomatic Protection Command, was detained on suspicion of murder and kidnap.
Prime minister Boris Johnson said he was “shocked and deeply saddened by the developments in the Sarah Everard investigation”, adding “we must work fast to find all the answers to this horrifying crime”.
A woman in her 30s has been arrested on suspicion of assisting an offender.
Everard's disappearance has drawn more attention to the dangers women face when walking at night.
Met Commissioner Cressida Dick said: "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."
The officer, who is in his 40s, was responsible for patrolling diplomatic premises but the Met did not provide specifics about his role.
His unit guards the Palace of Westminster, Downing Street and embassies in London.
He was not on duty at the time Everard disappeared and he has also been arrested for a separate allegation of indecent exposure.
Commissioner Dick said the news had "sent waves of shock and anger" through the public and her force.
"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," she said, adding that it could take hime to identify the remains.
However, former Labour minister Harriet Harman told MPs: "Women know abduction and murder is just the worst end of a spectrum of everyday male threat to women.
"When the police advise women don’t go out at night on their own, women ask why do they have to be subjected to an informal curfew?"
The home secretary said "every woman should feel safe to walk our streets without fear of harassment or violence".
In a statement, Priti Patel said: "I am deeply saddened by the developments in the Sarah Everard investigation. My heartfelt thoughts and prayers are with Sarah, her family and friends at this unbearable time.
"Many women have shared their stories and concerns online since Sarah’s disappearance last week. These are so powerful because each and every woman can relate. Every woman should feel safe to walk on our streets without fear of harassment or violence.
"At this deeply sad and tragic time as we think and pray for Sarah and her family, I will continue through my role to do all I can to protect women and girls from violence and harassment."
Labour leader Sir Keir Starmer said: "This awful news has shaken us all. I'd like to say these incidents are rare, but the truth is that violence against women and girls is far too common.
"No woman should walk home with fear or threat."
Everard's journey should have taken 50 minutes, and she was last seen on footage captured by a doorbell camera on the A205 Poynders Road towards Tulse Hill around 9.30pm.
The Telegraph reports that it is understood bus CCTV footage from the busy A205 route led to a breakthrough after examination by detectives.
A tribute at the woodland site in Ashford said: "Sarah, we may be strangers but all I can do is hope it's not you.
"Our hearts are breaking thinking of your poor family."
Women have shared their experiences of worrying encounters, feelings of apprehension and precautions they should not need to take when walking at night on social media.
A vigil called Reclaim these Streets has been organised at the bandstand in Clapham Common for 6pm on Saturday.
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."