Following advice in an earlier thread about extreme condensation in a sectional concrete garage, I tried laying a plastic membrane sheet over the entire floor area. This reduced the problem almost to zero - and when I lifted the sheet I discovered a standing pool of water underneath it. Clearly the water is seeping up through the base.
So the next step is to dry everything out and then apply some sort of sealant or floor paint. And maybe increase the ventilation too, for good measure.
Thanks to everyone who chipped in with thoughts and suggestions.
Bert