I would still think carefully about the condition of your walls and roof in terms of water ingress possibility, as this has a high chance of being a causative factor.
If you can get hold of a thermal imaging camera to point at the wall, that may give you some clues.
Log burners give off a large amount of heat in a relatively short time. If you have doors open in unheated rooms with cold walls and the significant heat from a log burner suddenly comes into contact with those walls, you get condensation. In our previous bungalow we had a very efficient log burner that I'd had installed in order to heat the entire property. Trouble was that once the heat from the log burner had built up in the lounge and I opened the door into the unheated bedroom, the walls began streaming with condensation. I cured the problem by having a radiator installed in that bedroom so that the temperature was maintained at a level where condensation couldn't form when the door was opened to allow the heat from the log burner into the room. I had a simultaneous problem with condensation in the loft because of excessive heat from the log burner rising through the ceilings and loft hatch and coming into contact with the cold underside of the roof sarking, but I cured that by increasing ventilation with soffit vents as well as cutting down on the use of the log burner.
If you plan on continuing to use the log burner, then you really do need to find a way to heat the entire property to eliminate the conditions in unheated rooms that create mould, and that probably means using the CH.
If you need to find a tradesperson to get your job done, please try our local search below,
or if you are doing it yourself you can find suppliers local to you.
Select the supplier or trade you require, enter your location to begin your search.
Please select a service and enter a location to continue...
Are you a trade or supplier? You can create your listing free at DIYnot Local