The force referred itself on Monday over the Fletton incident, the IOPC said.
IOPC director Emily Barry said her teams had been working closely with the force to “ensure that any complaints or conduct matters identified in its review are referred to us”.
“We will keep the complainant and the force updated as our investigation progresses,” she added.
Police have confirmed they are reviewing whether the Fletton incident is connected with the train attacks.
An IOPC spokesperson said: “We understand from the complaint that police were called by a member of the public to a report of a man armed with a knife.
“Prior to the police arriving the complainant reports he was punched by the man leaving him with facial lacerations.
“Police attended and spoke with the complainant however, the suspect had left the scene before officers arrived, and no arrest was made at the time.”
Meanwhile, British Transport Police has linked the train attacks suspect with two incidents in which a man entered a barbers’ shop in Peterborough earlier that weekend – as well as the stabbing of a 14-year-old boy.
Anthony Williams, 32, has appeared in court charged with 11 counts of attempted murder over the Huntingdon incident and a second stabbing in east London.
