The problem you describe is probably as you suggest, condensation. Using LPG causes a large amount of extra water vapour to be released into the atmosphere thus making the condensation worse. Electric heating would add no water vapour to the atmosphere. Hot air can carry more water vapour than cool air. As air cools the water vapour condenses onto the coldest surfaces in the room .. such as glass and cold stone walls.
If you think of dampness as being water where you do not want it and a major cause was water coming through the wall the application of a water repellent would solve it. This would not solve the problem you describe. It would help though, treating the outer face of external walls with a water repellent can be very helpful because water saturated walls have a lower average temperature and as such lose heat more rapidly.
You have additional problems to do with the surface temperature of walls and windows and the amount of water in the atmosphere – relative humidity. External walls, ceilings which are the underside of the roof and floors directly onto rock are a big problem in Malta because there is a history of not having or having inadequate insulation. The problem is not peculiar to Malta but most countries in northern Europe have an enforced building code ensuring a decent standard whereas in Malta builders and architects largely, do their own thing.
The benefit of insulation is not limited to winter time, good insulation will help keep summer temperatures lower and more comfortable.
What can you do? Do an internet search on condensation cures, but when condensation problems are severe do not use LPG. Usually constant 24 hour heating at a low level is better than intermittent heating at higher levels. A dehumidifier is good because it lowers the moisture in the atmosphere and some of the electric used is given off as heat. If practicable interior insulating of the walls and ceiling can make a big difference but ensure that foil backed plasterboard or similar is used to stop water vapour migrating through the finished surface and condensing behind. The most effective way of insulating is externally but this is often too difficult to achieve in existing structures.
Good luck. Steve