I am on this cruise Costa Allegra) on Jun 2nd, but looking at some of the destinations I think you'll be hard pushed to find a cash point. Costa have also said that they will be carrying limited funds onboard so not too rely on them for all your cash.
As you're probably visiting a number of different countries, you're better taking travellers cheques and converting them as you go along on board the ship - the post office offers the best rate of exchange if you have any left over when you get back. Alternatively, you could always just rely on your debit/credit card, you'll most probably be able to find a cashpoint in every port and most shops take payments using visa/mastercard. Tip - Nationwide don't charge you for using your card abroad.