Parents and pupils were “shocked” when a fight broke out at the end of the school day outside Denbigh Primary School on Friday.
A group of about eight people were involved in the brawl in Denbigh Road at abot 3.15pm.
It is thought the fight started after two men were involved in a parking dispute as pupils were leaving the school.
More people became involved in the argument and started fighting and it is believed some parents filmed the disorder on their mobile phones.
PC Nick Foster said: “At this stage no one appears to have been seriously injured during the incident but it was a shock for parents and pupils to witness. Four people have been arrested in connection with this investigation but we need further information from the public. We believe some of the parents may have recorded the incident on their mobile telephones and I would ask these people to contact us as their footage may help identify those involved.
Anyone with information relating to this incident can contact PC Foster, in confidence, on 01582 394191, or Bedfordshire Police, on 101, or text information to 07786 200011.
Alternatively, contact the crime fighting charity Crimestoppers, anonymously, on 0800 555 111.