Officers chased a group of teens through the North Laine and into The Lanes after reports of a youth with a knife.
Police are now appealing for witnesses to the brawl which sparked the chase.
A member of the public told officers on patrol in Trafalgar Street at about midday on Thursday, 13 July.
Officers gave chase on foot along Tidy Street and into Meeting House Lane.
An 18-year-old man was arrested on suspicion of affray, possession of an offensive weapon in a public place and being concerned in the supply of Class A drugs.
A knife and a package containing Class A drugs were found nearby.
Witnesses, including drivers travelling along Trafalgar Street at the time who may have relevant dash cam footage, are asked to contact police online or via 101, quoting serial 638 of 13/07.
