Police were called at 12:41pm on Saturday, 26 October following reports of a fire in a flat on Mingard Walk, N7.
Officers attended along with the London Ambulance Service and the London Fire Brigade.
Formal identification is yet to take place, but officers are confident that a woman pronounced dead at the scene was the occupier of the flat, 59-year-old Beatrice Yankson
A post-mortem examination which took place on Tuesday, 29 October, established cause of death to be burns and inhalation of fire/fumes.
A man, believed to be aged in his 30s, was found suffering serious injuries. He was taken to hospital in a critical condition, where his condition remains unchanged.
Homicide detectives from Specialist Crime are leading the investigation and are appealing for any witnesses to come forward.
Detective Chief Inspector Paul Considine said: “We believe this fire was started deliberately which is why it is being investigated as a murder.
“Our thoughts are with Beatrice’s family, and we are working hard to understand the series of events which led to her death.
“We would like to thank the residents of the block, who were evacuated as a precaution and who have provided assistance to officers so far.”
Anyone with information should call the incident room number on 020 8345 3865 quoting Operation Rushville.