At approximately 20.15hrs on Sunday, 20 February, police attended an address in Oakridge Road, Downham, after concerns were expressed over the welfare of the occupant.
London Ambulance Service also attended and on arrival officers found a woman suffering head injuries. She was pronounced dead at the scene.
The victim has been identified as Jean (known as Pat) Jobson, 86. Next of kin have been informed.
A post mortem examination will begin at 0900hrs on Tuesday, 22 February, at Greenwich Mortuary.
Officers from the Homicide and Serious Crime Command are investigating and an incident room has opened under Detective Chief Inspector, Cliff Lyons