Have I got Rising Damp or a leak?
If this is a fairly sudden change or it's very localised then it could indicate a leak or overflowing gutter etc.

If it's always been this way, the problem is more widespread or the change has been very gradual then it's more likely to be damp. Are any areas of the house below ground level? Or has the ground level been built up along that wall? The cure could be as simple as digging some soil away from the walls, to make sure that the existing damp proof course hasn't been bridged. This will stop any more moisture getting in and allow the rooms to dry out.

If none of these simple remedies work, I'd call in at least two professionals to give quotes. If they give wildly different possible causes then get a third. Fixing damp can be expensive and if you get it wrong and it doesn't actually cure the problem.