A significant source of damp can be a high ground water level under a stone floor slab, or a conventional wooden floor construction over bare earth.
Warming the rooms up can raise humidity levels and despite obvious ventilation, etc, dehumdifiers may have to be used.
Owning two very damp properties since 1980, I am using small but very effective portable domestic dehumidifiers that I purchased in 2008.
They are plugged in all the time and switch themselves off when the removable ‘collector’ is full or they get knocked over. They do not get hot and are low wattage (70W).
My current model is a Slemcka small portable dehumidifier for the home. There are similar models on the market.