Some 78 passengers have already been reported to have been taken ill with the norovirus type infection since the ship set sail for a 16-day Christmas cruise.
The 90,000-tonne liner, which has been in operation for less than a month, was launched from Southampton by the Duchess of Cornwall.
Some passengers who paid between £1,100 and £24,400 each for the cruise have now said they will be seeking compensation over the outbreak.
Jean Trainor, 49, from Blackburn, Lancashire, told the Daily Mail newspaper: "No hygiene rules were implemented until people fell ill.
"If they had been, maybe this could have been avoided."
Clive Garner, Head of Travel Law at National law firm Irwin Mitchell, said:
"Each outbreak of illness brings great misery for people who have spent a large amount of money on what they had hoped would be a dream holiday. "
"Last year the travel law team at Irwin Mitchell dealt with many outbreaks of illness on board cruise ships, more than we had ever seen previously."
"Because people are in confined areas onboard cruise ships they are highly susceptible to viral contamination. Cruise ship operators must take special care to control outbreaks of illness and take all reasonable steps to minimise the risk of passengers becoming infected. We welcome the publication by the Health Protection Agency of of its guide for cruise ships on how to prevent and control infections. We hope that the guidelines will improve heath conditions and reduce the incidence of future problems on board cruise liners.".