Laura Cecilia Navarrete De Figueira, 47, her husband Adelino Gabriel Figueira de Faria, 57, and their children Claudio Gabriel, 10 and Joaquin Alejandro, seven, were found dead on 5 March.
Police found the bodies of a man and two boys just before 5pm on the beach at Birling Gap seafront in East Sussex.
Ms Navarrete De Figueira’s body was found at around 6pm when police arrived at her home in South Road, Twickenham, southwest London, after concerns were raised about the family’s welfare.
She was found dead at the scene with stab wounds.
The bodies at Birling Gap were later confirmed to be the woman’s husband and two young sons, after Sussex Police contacted Scotland Yard when they learned officers were looking for a man and his two sons.
A post-mortem examination found that Ms Navarrete De Figueira died from multiple stab wounds.
An examination of Mr Figueira de Faria showed that he died from multiple injuries consistent with falling from height.
The same cause of death was given for the two boys.
More from UK
Specialist team to assess scale of Telford sex abuse cases
Teenagers hunted after ‘sickening’ attempted murder on tram platform in Greater Manchester
Westminster terror attack: #LondonUnited one year on
Murder suspect claims torched nanny betrayed her to win Tom Cruise film role
120 firefighters tackle ‘massive’ blaze on Glasgow’s Sauchiehall Street
Friday’s national newspaper front pages
Officers from the Met’s Homicide and Major Crime Command are leading the investigation, supported by Sussex Police, and police are not looking for anyone else in connection with the deaths.
Anyone with information is asked to call the Metropolitan Police or Sussex Police on 101 or Crimestoppers anonymously on 0800 555 111.