Police officers on horses eventually managed to break up the brawl by using batons as one man walked away with a nasty gash down the side of his face.
Following the fights, a police spokesperson confirmed that the knife injury sustained by one supporter was not thought to be life-threatening.
The Metropolitan Police released a statement on the incident that read: 'At around 16:42hrs officers became aware of a large group of males fighting in the Hawkstone Road area.
'One male aged in his 20s was discovered suffering from a slash wound to the face. He was taken by LAS to a south London hospital. His injuries are not life-threatening.
'A crime scene remains in place. Officers worked to separate the groups with support from the Mounted Branch. At this early stage, there have been no arrests.'