Police were called at approximately 02:35hrs on Sunday, 10 February, to reports of a man stabbed on Lordship Lane, near the junction with East Dulwich Grove, SE22.
Officers and the London Ambulance Service attended.
Whilst we await formal identification, detectives are confident the deceased is 39-year-old Dennis Anderson, from Lewisham.
A post-mortem examination is due to be held on Tuesday, 12 February.
Detective Inspector Domenica Catino, from the Met’s Homicide and Major Crime Command, who is leading the investigation, said: “We need to hear from anyone that may have been in the area on Sunday morning who may have information on the circumstances of this tragic turn of events. Any information, no matter how insignificant it may seem, could really help our investigation.
“We are aware of speculation around the motive for this attack and can now confirm that the suspect approached Mr Anderson in an off-licence shop before an altercation broke out and the suspect delivered a fatal attack.
“Our top priorities now are to support Mr Anderson’s family and catch the person responsible for this horrible attack. Officers are working around the clock to locate this suspect and bring him into custody.”
Anyone with information is requested to call police in the incident room on 020 8721 4961.