Officers were called to a pub in Chislehurst just before 9pm on Friday following reports of men fighting.
Minutes later, a man in his 30s was killed after being struck by a pickup truck less than a mile from the scene.
The van did not stop and was later found abandoned near the scene of the collision, a police spokesperson said.
Two men were found at the nearby Gordon Arms pub with stab wounds and were taken to hospital. The police make the connection between the incidents.
A Met Police spokesman said: “Police were called at 8:52 pm on Friday July 24 to Belmont Road in Chislehurst following reports of men fighting.
“At 8:54 pm, police were alerted to a collision involving a van and a pedestrian near Slades Drive, Chislehurst.
“The pedestrian, a man believed to be in his thirties, died at the scene. ”
He added: “The investigations are in their early stages, but these incidents are currently being treated as related.
“Extensive cordons and road closures are in place as investigations continue. There were no arrests. ”
Anyone with information on either incident is urged to contact police on 101, citing CAD 8031 as of July 24.