The 2006 Commonwealth Games gold medallist, real name James Russan, was charged following an incident on Lambeth Road, Kennington, on 16 July.
Mr Cox, 28, is charged with common assault, violence to secure entry, harassment and criminal damage.
The case at Camberwell Green Magistrates' Court was adjourned.
He is due before Croydon Magistrates' Court on 12 January, 2016.
The WBO European super-middleweight boxer Jamie Cox has appeared in court following an alleged assault in south-west London.