Palmira Silva (pictured above), 82, who is believed to be of Italian descent, was found dead outside in a suburban back garden.
Tributes were paid to Ms Silva, who is thought to have worked in a nearby cafe, as a 25-year-old man held in connection with the killing remained under police guard in hospital.
The man was Tasered and arrested on suspicion of murder at the scene in Nightingale Road by armed officers, some of whom were injured in a struggle.
Police say they do not believe there is a terrorist motive but have not confirmed if Ms Silva, who was pronounced dead at the scene, was beheaded.
Detective Chief Inspector John Sandlin, who is leading the investigation, described it as a “highly visible attack in broad daylight”.
He added: “I can understand why this may cause people concern, however we are confident that we are not looking for anyone else at this stage.
“Whilst it is too early to speculate on what the motive behind this attack was I am confident, based on the information currently available to me, that it is not terrorist related.
“Local officers and specialist detectives are at the scene and will remain there for many hours to come.”
Scotland Yard revealed that its officers distracted the man after he was seen going through back gardens in Nightingale Road to prevent him attacking anyone else while they evacuated people from nearby homes.
Officers from the Met’s homicide and major crime command are also investigating an attempted attack on two people at another house in the road before Ms Silva was killed.