The incident happened in Tooley Street, Bermondsey at around 9pm yesterday (August 20).
Officers attended and found two men, both 23 and another man, 31, injured.
They were taken to hospital where their injuries were declared non-life-threatening and non-life-changing.
The three men were initially arrested on suspicion of possessing an offensive weapon, but were subsequently dearrested.
Police enquiries continue.
A spokesperson for Metropolitan Police said: “Anybody who witnessed the incident, or who has information, should call 101, quoting 7740/20AUG.
“Alternatively, an anonymous report can be filed via Crimestoppers on 0800 555 111.”
A spokesperson for London Ambulance Service said: “We were called at 8.56pm to reports of a road traffic collision at the junction of Tanner Street and Tooley Street, Bermondsey.
“We sent a number of resources to the scene including ambulance crews, paramedics in fast response cars, advanced paramedics and incident response officers.
“We treated three patients at the scene and took them all to a major trauma centre as a priority.”
