At around 11:30pm a group of men were inside KFC at the Xscape building when another group began shouting at them from outside.
Security staff intervened but the group inside the restaurant forced the door open, causing the glass to smash.
As the group inside left, both groups then approached a taxi in the car park. As some of the group got in, the other group smashed the rear window of the taxi.
The two groups then began fighting and had to be separated by security.
No injuries have been reported as a result of this incident.
Investigating officer PC Dean O’Dell, based at Milton Keynes police station, says, “I am releasing these CCTV images as I believe these people will have vital information to help with the investigation into this offence.
“This incident happened when the area was busy and I am keen to hear from anyone who witnessed the incident or has any information about the events leading up to it.
“You can share information with us using our online form or by calling 101. You will need to quote reference number 43190072881. Alternatively, you can contact Crimestoppers anonymously on 0800 555 111.”