The incident took place near the taxi rank at around 10.45pm on Saturday 5 June.
It was reported that a group of males approached another group of people and a fight then took place.
A 35-year-old man and a 36-year-old man, both from Basingstoke, sustained facial cuts which required treatment at hospital.
No arrests have been made.
Police are investigating the circumstances of this incident, and we would like to hear from anyone who saw what took place.
Anyone with information should call police on 101, quoting the reference number 44210219911.
Alternatively, people can call Crimestoppers on 0800 555 111, where information can be left anonymously.