Detective Superintendent Rob Vinson, who is heading the investigation for the Kent and Essex Police, told the Harlow Star the deaths are being investigated as murder Wednesday.
Dr. Sabah Usmani, 44, and three of her children were killed in the Oct. 15 fire, while the other two children died two days later. Dr. Abdul Shakoor, who returned home to find his house in Harlow, Essex, on fire, suffered smoke inhalation and burns trying to save his family.
Vinson, who also appeared on the BBC "Crimestoppers" program, said a laptop computer belonging to Abdul Shakoor was stolen from the room where the fire began.
The laptop's case was discovered in an overgrown area 11 days later, but the computer is still missing. Vinson appealed to anyone who might have been offered a Toshiba Satellite laptop for sale or seen anyone getting rid of the case to come forward.
"This was a terrible tragedy in which a mother and her five children have died and a husband and father has lost his entire family -- someone out there must know something," he said.
The Crimestoppers charity has offered a reward for information leading to arrests.