Hey AnneG, we had similar problems in several of our flats. A couple thoughts:
First, be careful sealing the windows too much. Cooking, laundry drying, breathing all contribute to damp
inside the house. Sealing the windows will just keep it in and give you worse problems like mold growing on walls between them and your furniture.
A good de-humidifier should tell you what sort of area it will cover. If your house is small, one may do the trick. Especially if you can have it somewhere near the stairs. We had one in our last flat and lemme tell you, we emptied it all the time.
Do open a window at least once a day - especially when cooking (if boiling water in particular) and when drying clothes.
Do run the heat whenever you can.
Look for a new place as soon as possible but be very careful - our experience has been that inevitable we exchange one set of problems in rented accomodation for another.
Your landlord is typical of every British landlord I've ever encountered in the UK. The least amount of attention to the property for the most rent.