Officers from the Metropolitan Police were called at 11.19pm on June 11 with reports of an incident in Claxton Grove.
At the scene, two men were found being treated for gunshot wounds before being taken to hospital.
One of the victims, a 30-year-old man, died in hospital the following day (June 12).
His next of kin have been informed and are being supported by specialist officers. A post-mortem examination will take place in due course.
The second man, also in his 30s, was treated for minor injuries and has been discharged from hospital.
A 28-year-old man was arrested on suspicion of attempted murder. He has since been re-arrested on suspicion of murder, and remains in police custody.
Det Chf Supt Christina Jessah said: “Our deepest sympathy is with the victim’s family who are being supported by specialist officers at this time.
“This is a shocking crime to occur in any community, and we thank locals for their patience. They will see an increased police presence in the area as we conduct our enquires.”
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If anyone witnessed the incident, or has any information that can help the investigation, please contact the police as a matter of urgency on 101 quoting 8916/11JUN.
To remain anonymous, call the independent charity Crimestoppers anonymously on 0800 555 111 or visit crimestoppers-uk.org
Claxton Grove will remain closed while a crime scene is in place.
