A man, 43, and a 41-year-old woman have been arrested on suspicion of assault.
Good Morning Britain journalist Richard Gaisford, who was on board, said an emergency tannoy summoned security staff to the ship’s restaurant in the early hours of Friday.
Writing on Twitter, he said: “Witnesses told me they were so frightened they had to hide, as family groups fought,” he said.
The people suspected of being behind the violence were confined to a cabin for the last day of the cruise, Mr Gaisford said.
He said the violence occurred after a black-tie evening and an afternoon of “patriotic” partying on deck, when large amounts of alcohol were consumed.