Hi, we cruised on the The Destiny in October 2007. They will accept Debits cards for all your on board accounts. We are doing another cruise in December again on the Destiny, once again we will be using our Debit card with no problem at all. You sign for all of your purchases on board then at the end of your cruise, and when you return home it will be debited from your account. I also settle my final invoice by Debit card as they do not charge for that as they do for Visa or any other credit card. Hope you enjoy your cruise.
All you purchase on the ship drinks; items from the shops etc are charged to your cabin account which is settled before you leave. You will get a receipt keep these safe in case you have a query. Effectively you are joining the cashless society at least for the duration of your cruise. Normally they prefer credit cards; travellers cheques or cash but you will find out when you check-in if they will accept your debit card but I would have one or more of the options above if they don't, or ask your travel agent to advise or contact Thomson cruises direct and or check the booking details in their brochure.
I'm not aware of any cruise line that accepts Debit cards for on board accounts. You need to check if that's your only card.
We have cruised with Thomson since 2005 on the Destiny, Celebration and Emerald and have always paid by debit card. Under the section 'All you need to know' and then 'Money matters aboard ship' at the back of the Thomson brochure tells you what you need to know.