Police were called to a business premises in Long Lane, Southwark, at 1pm on Monday, where they found four people had been stabbed.
A 58-year-old man died at the scene while three others were taken to hospital, the Metropolitan Police said. These included a 27-year-old man who has since died.
A third man, who is in his thirties, remains in hospital with injuries described as non-life-threatening.
Another man in his thirties, who has been detained in connection with the incident, remains in a life-threatening condition in hospital.
Detective Chief Superintendent Emma Bond said: “Our investigation is in the early stages and we are working hard to understand the full circumstances of this shocking incident.
“At this point, we do not believe it to be terrorism-related and there is no further risk to the public.”
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