It comes after the Metropolitan Police were alerted to concerns for the welfare of a person at an address in Argyll Road at 5.25pm on January 17.
Officers attended and gained access to the property, discovering a 43-year-old woman dead inside.
Her next of kin have been informed, though formal identification is yet to take place.
A post mortem examination held on January 18 gave the cause of her death as blunt force trauma and head injury.
Police believe the suspect was known to the victim, but there have been no arrests made in connection to the murder investigation at this stage.
READ MORE: Murder investigation launched after woman, 43, found dead in Woolwich
DCI Suzanne Soren, Specialist Crime South, said: “This is a deeply tragic incident and are thoughts are very much with the victim’s family who are being supported by specialist officers.
“At this early stage we believe the suspect was known to the victim and we are carrying out urgent enquiries to trace a named individual.”
Anyone with information that could assist the investigation is asked to call 101 quoting reference CAD 5231/17Jan.
