The ship docked after a 10-night Baltic cruise, Sky News reported.
Norovirus is highly contagious and causes vomiting and diarrhea.
The company's owner, Carnival, first said there had been "an incidence of a mild gastrointestinal illness" among the 1,800 people onboard. An official later apologized to the passengers.
"It has been outrageous from start to finish," passenger Paul Gilman said. "People were falling like flies, yet the crew were trying to insist everything was fine. Everyone is saying, 'This is a plague ship.' It's a living nightmare."
Carol Marlow, managing director of P&O Cruises, said the ship underwent a "full sanitization process" before it set sail from Southampton Dec. 4. She said the first cases of norovirus, which has an incubation period of one to two days, were reported within hours of the vessel's departure, indicating the virus was brought onboard by one of the passengers.
Marlow issued an apology: "We don't want one person to be ill on any of our holidays and we'll learn from this and try to make sure it doesn't happen again."