Police arrested a 40-year-old man Tuesday on suspicion of murder after a woman was stabbed to death and two others injured in a knife attack in south London.

A 46-year-old woman is in a critical condition in hospital after being stabbed multiple times in the first attack at a flat in Brixton on Monday evening, Scotland Yard said.

The woman was rushed to a south London hospital after police and paramedics were called to the housing block in Redlands Way at around 6.40pm.

About half an hour later, officers were called to a flat in nearby Tilson Gardens where another two women had been attacked.

A 28-year-old woman was pronounced dead at the scene and her 17-year-old sister was taken to a south London hospital where she is said to be in a serious but stable condition.

London's Metrpolitan Police said a man arrested on a bus in the early hours of Tuesday was held in custody at a south London police station.

Detectives are not seeking anyone else in connection with the investigation, the force said.

"Our investigation is at a very early stage, however we are confident that there are no outstanding suspects," said DI Will Reynolds, of the Met's Homicide and Serious Crime Command.

"We believe that all three victims were known to the man who is currently in our custody -- there is no suggestion that the victims were selected at random."

Reynolds said the teenage girl was stabbed in the head and hands while trying to protect her older sister.

Hawa Musse, who lives at Tilson Gardens, said she came out and found the injured girl outside the flat after hearing a boy screaming from a balcony.

"She was sitting on the floor," she said. "There was a lot of blood coming from her head. She was saying 'My sister is inside'."

Chuka Umunna, the local MP and shadow business secretary, visited the crime scenes Tuesday.

He said: "I think the community is deeply shocked and traumatised by what has happened in our area.

"I think the most disturbing thing is the ferocity of violence which occurred and which was witnessed by young teenagers and children on the two estates."