Call the helpline 0845 3 555 800 and ask that way your mind at rest as you will have the company's response but I should think it would be fine, but then we always use credit cards.
Yes ring - I don't think they accept ANY debit cards only Credit cards. The reason is simple. You register the credit card at the start of the cruise and they can check to see it has credit on it before they open your account also because it is a credit card there is more certainty of payment. A debit card is like cash, it deals with what is on your bank account that day and it debits your account immediately. The ship cannot therefore be as certain that there will be any money in your account on the day they debit your account. The other thing is that they would have an enourmous amount of work to do before you left the ship in order to try and process potentially thousands of payments instantly. At least that is what I surmise is the reason. If you do not want to use a credit card (or dont have one) there is not time to get one (I reccomend nationwides as there are no exchange charges). Instead I would buy Dollar Travellers cheques having estimated how much you are likely to spend (include shore excursions) then pay these into your shipboard account when you board. Ask for updates on your account to keep a check on things!! Remember you can use your debit card in ports to take out money up to your daily limit to top up your account/spending money. Tell your bank you are going abroad and take their Debit Card 24hr helpline number with you in case they temporarily block your card through 'unusual usage'.