Chris, assuming that there is no actual water ingress through roof/walls/floor, then it just a case of controlling the humidity level. Slightly easier said than done mind.
If you are willing to through some cash at it, then you need to look at insulation, ventilation, back ground heat.
In the first instance and as a cost effective starting point I would look at putting a decent de-humidifier in there. Once this has had a chance to dry things out and lower the humidity then you can tackle the problem.
Damp Proofing, Condensation control and water proofing was what I did prior to encountering my current health problems. Let me know if you want any advice, always happy to help.