To reduce damp: heat or dehumidifier?
With "damp", your enemy is humidity, or water which is dissolved in the air.  Warm air can disolve a lot more water than cool air.  When warm, water-saturated air moves to a cooler place, it cools the air.  The water cannot remain in the air, and must condense, typically on a cool object.  

A heater raises the air temperature, which temporarily increases its capacity to carry water. Since it is laboring to keep the water in the air, it must do that continuously.  A dehumidifier removes the water from the air, so it only has to do that job once until the air changes.  

As a bonus, all the electric energy the dehumidifier uses, does go to warm the room.  Not the most efficient if you were only looking for heat, but for removing water it's not bad.