Take a look at the MSC Orchestra. It is being advertised as "Child Free" all year! Happy cruising.
If you have as little luck finding out any more about this as I have, then I would recommend looking at the two P&O ships Arcadia and Artemis. Both are child free, the Arcadia being the larger and more modern of the two. They cruise from Southampton during the summer and Caribbean during the winter. I believe that Thomson run some child free cruises on various ships from time to time also. Happy cruising.