The bodies of two young boys and their father were discovered at the foot of cliffs on the south coast an hour before their mother was found dead more than 80 miles away.
Scotland Yard said a murder investigation had been launched after the woman, believed to be in her 40s, was found with stab wounds at her home in South Road, Twickenham, south west London shortly before 6pm on Monday.
Detectives attempted to trace her husband, 57, and two boys, aged seven and 10, and were later contacted by Sussex Police about the discovery of three bodies earlier that day.
Officers had been called by a member of the public who found a man and two children dead on the beach at the foot of cliffs at Birling Gap, in Eastbourne, East Sussex, shortly before 5pm.
A Metropolitan Police spokesman said: “Whilst formal identification awaits, police believe that they are the deceased woman’s immediate family.”
No arrests have been made and the Met said officers are not looking for anyone else in connection with the investigation.
The London home – which neighbours believe was rented – remained sealed off with police tape and had a significant police presence outside on Tuesday afternoon. Officers in forensic uniforms were seen inspecting the front garden and bins.
Paul Warrington, 54, a graphic designer, said: “They were just a very normal family. There was nothing to suggest anything untoward.
“They kept themselves to themselves. We have a residents’ association here and they never got involved with that.
“We used to see the kids and hear them playing in the garden. They were just normal kids making a lot of noise screaming and playing.
“It’s just absolutely horrible.”
Alicia Mede, 25, a mother of two who lives two doors down, said: “I didn’t even know anyone lived there. I have never seen any kids living there or anything.
“I saw Christmas lights on around Christmas time, but that was it.
“I haven’t seen anyone come or go.”
A spokeswoman for the force added the three bodies had not been found in the vehicle.
Post-mortem examinations have yet to take place and next of kin have been informed.