You can buy some anti-humidity device which is quite cheap, from any DIY shop, and just leave it there to absorb the surrounding damp. You will just need to empty it regularly of its captured water content and add new tablets, but that is pretty much all that's required.

Not an expert but some times doing the little things yourself can help. Check out youtube. That is offcourse dependent on how much time you both bave.

Have!!!!

You can also try putting an electric dehumififier in your basement and seeing how quickly it fills the container with moisture that it extracts from the air.  

Also it's worth trying to identify where the damp is coming from.  Is it rising from below, or is it entering via the walls?  Is there enough air-flow through the basement?  Each of these situations would have different solutions.