Cellars are always going to be prone to damp, but they can be sorted out. It's worth doing too, because they are naturally very well soundproofed.
I just went through analysing and sorting out a damp problem - in my case it was rising damp, but the causes were the same. In doing research on dampproofing, I ran across a lot of articles and videos on cellar problems. Here's a good one which lines up with everything I've read:
http://www.familyhandyman.com/basement/affordable-wet-basement-solutions/view-all
It's usually construction issues (lack of damp courses, improper drainage, etc. and, while it's not always possible to go back and redo the construction, you can do a lot to alleviate the problem. As always, prevention is better than cure and attacking the problem rather than the symptom is the wisest approach.
Primary things to do are: get as much water away from the foundation as possible; seal any cracks; damp seal the walls; insulate the walls and floor; and finally, install aircon/dehumidifier in the room.
