OK first off the problems may not be connected.
Let's start with the main house. What's it made of (i.e. is it a standard brick cavity? does it have insulation in the cavity, when was it built?)
Generally the problem is lack of ventilation, people close all the windows to "keep the heat in" - never a good idea as you keep all the humidity in as well and it quite naturally condenses on the colder surfaces. One way around this is to use a dehumidifier (which will add to your energy bill) or as you've mentioned to improve ventilation. You can often do this by opening transom (fan-light) windows a little in a few rooms. You'd be amazed the difference it that can make. Of course bathrooms need to be ventilated and a fan is by far the best option for this.
If there is excess moisture then get somebody in to check the internal walls to see how damp they are.
If the utility room is single skin you might be suffering from penetrating damp as well as from the effects of a tumble drier etc. Again ventilation is the answer, maybe using an expelair fan or similar that works when the room is in use. You could also try a water proofing product from Thompsons on the outside of the building.
Can't really say more until the question at the top of the post is answered.