The 62-year-old woman found dead in a house in Colliers Wood has been named as Jill Grinstead.
Yesterday a 37-year-old man from Colliers Wood was arrested in connection with the inquiry. He is being interviewed at a south London police station.
The investigation was launched after the woman's body was discovered at a house in Laburnum Road, Colliers Wood, on Thursday.
Officers were called to the house at around 9am on after a neighbour noticed that the door to the property was open and the front window smashed.
A post-mortem at St George's Hospital mortuary gave the cause of death as asphyxia and blunt facial trauma.
DCI Mick Duthie, of the Homicide and Serious Crime Command, said: "Various residents have reported hearing suspicious noises through the night such as glass smashing and raised voices, perhaps in an argument."
Police are appealing for anyone with information to come forward, especially people who were in the quiet residential area, just off Merton High Street, between 9pm on Wednesday and the early hours of Thursday morning.
Anyone with information should contact the Incident Room at Sutton on 020 8721 4155 or Crimestoppers anonymously on 0800 555 111.
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