Police were called at 10.57pm s on Thursday, 1 October to reports of a stabbing in the communal area of flats on London Road in Morden.
Officers and the London Ambulance Service attended. Two men were found with stab wounds.
A 25-year-old man was pronounced dead at the scene at 11.26pm. Enquiries to inform his next of kin are ongoing.
Formal identification awaits. A post-mortem examination will be held in due course.
A second man, aged 33 was taken to hospital. His injuries are not thought to be life-threatening.
A crime scene remains in place.
Homicides detectives from the Specialist Crime Command are investigating.
Anyone with information is asked to call police via 101 quoting reference Cad 7953/01Oct. Alternatively, to remain anonymous call Crimestoppers on 0800 555 111.
No arrests have been made and enquiries continue.