The victim – named by friends as Maureen Watkins – died after being attacked at a house on Ethnard Road in Peckham shortly after 4pm on Friday afternoon.
A 55-year-old man – believed to have known Ms Watkins – was arrested at the scene on suspicion of murder.
Medics said the victim had received multiple stab wounds. Despite efforts to save her, she was confirmed dead a short time after ambulance crews arrived.
The suspect was taken to an east London hospital to be treated for a stab wound before being taken to a south London police station, where he remains in custody.
Ms Watkins was said to have lived at the terraced property with her son for around 30 years.
“She was a lovely lady, a very nice lady indeed,” said a friend living nearby, who asked not to be named. ”It is very sad."
Another neighbour, who stopped to lay a bouquet of flowers at the property, said: “Maureen was lovely. I’ve been here since I was about four years old and she was here the whole time. I’ve always known her to say hello and that. I’m just shocked really.”
Detectives in the Metropolitan Police’s homicide and major crime command are investigating.
“The man and the woman were known to each other,” said a Met spokesperson. “No other persons are sought in connection with this incident.”
The violent death toll in London continues to rise, with the latest killing bringing the total number of homicides to 122 – more so far this year than in the whole of 2017.
A grim spate of bloodshed in the capital saw five separate stabbing deaths in the week from 31 October.
Mr Javid said the police needed to “step up the response to get the situation under control”.
Ken Marsh, chairman of the Metropolitan Police Federation, told The Independent politicians should “leave police alone and let us do our jobs”.
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