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The man was discovered injured in Southampton Way around 10.30 p.m. yesterday (June 22).
He was taken to the hospital, where he is still in critical condition.
There have been no arrests.
The Met's Central South Command Unit is conducting investigations.
Anyone with information that can assist police should call 101 and reference CAD 8254/22 Jun.
"Police were called to Southampton Way SE5 at around 10.30pm on Wednesday, 22 June to reports of a stabbing," a Metropolitan Police spokesperson said.
"A 20-year-old man was discovered with a stab wound.
"He was taken to the hospital, where he is still being treated for a life-threatening condition."
"No arrests have been made."
"Investigations are still ongoing, led by the Central South Command Unit."
"Anyone with information that could assist police should call 101 and reference CAD 8254/22 Jun."