Police were called at about 8.25pm on Monday, 14 February to a home in Congleton Grove, SE18.
The body of a woman, believed to be aged in her early 30s, was found inside the address suffering injuries.
Officers believe they know the identity of the woman and urgent efforts are under way to inform her family.
A post-mortem examination will take place soon.
Homicide detectives from Specialist Crime are investigating.
There have been no arrests so far and detectives are working to establish what happened.
At this early stage, anyone with information is asked to contact the incident room on 0208 721 4027.
Alternatively call police on 101 or tweet @MetCC and quote CAD 6610/14Feb.
To remain 100% anonymous contact the independent charity Crimestoppers on 0800 555 111.
