At around 8.20pm on Sunday 14 June, a man who was part of a group repeatedly punched a passenger in the face and head before leaving the train, walking along the platform at Highbury and Islington station, and boarding the same train again.
Once on board, he then assaulted another passenger before disembarking and moving to the next carriage and assaulting a third passenger.
The group of five, made up of four men and one woman, continued along the train, boarding another carriage and assaulting more passengers. Several victims were punched multiple times in the face and head, with one individual sustaining an injury to the eye. Four people required hospital treatment.
The group left Highbury and Islington station and were involved in another altercation outside.
Officers are appealing to anyone who may have witnessed or filmed the incident to contact them by texting 61016 or calling 0800 40 50 40, quoting reference 633 of 14 June.
Information can also be given to Crimestoppers anonymously on 0800 555 111.