Fred Olsen Sounds just what your looking for.
I would suggest you look at Fred Olsen's ships; some go from Southampton, some from Dover. Alternatively you could look at P&O's Artemis which is an adult only ship. I know Fred Olsen have ballroom instructors on board and although they do have children there are not usually many on board as most of the clientele are 50 and above. Fred Olsen is a very British line which sounds just what you are looking for.