A 24-year-old man was arrested on suspicion of murder after stabbing a man in East Dulwich.
Victim Dennis Anderson, 39, was approached by the suspect in a shop before a fight broke out, police say.
The police were summoned shortly after 2.30 am on Sunday to Lordship Lane, East Dulwich, near the intersection with East Dulwich Grove.
Anderson was pronounced dead at 3:04 am, Scotland Yard said.
He died of a stab wound on his neck.
Detective Inspector Domenica Catino of the Commander of the Met and Heavy Crime Commander of the Met, who directs the investigation, said, "Although we were arrested, we still have to hear from everyone who was in the area on Sunday morning.
"Any information, no matter how insignificant it may seem, can really help our investigation.
"We are aware of the speculation about the motive for the attack and can now confirm that the suspect turned to Mr. Anderson in an off-license deal before a dispute broke out and the suspect made a deadly attack.
"Our top priorities are now supporting Mr. Anderson's family."