Officers were called to Hawkstone Road shortly after 4.40 a.m. (June 23).
Paramedics from the London Ambulance Service were also present.
At 5.05 a.m., the man was pronounced dead.
His death is being investigated as unusual but not suspicious.
His next of kin has been notified.
A post-mortem examination will be performed as soon as possible, according to officers.
The coroner will be given a file.
“Police were called at 4.42am on Thursday, 23 June to reports of an unresponsive man in Southwark Park, Hawkstone Road,” a Metropolitan Police spokesperson said.
“Officers and London Ambulance Service were present.”
“At 05:05 a.m., the man was pronounced dead.”
“The death is being treated as unusual but not suspicious.”
“The man’s next of kin has been notified.”
“A post-mortem examination will be carried out as soon as possible.”
“A file for the coroner will be prepared.”