By downstairs do you mean in a basement? We had a basement room at our previous house and that could feel damp in the summer as the room walls and floor are relatively cool and the warm outside air is relatively humid causing condensation to form on everything in the room. Opening windows made it worse as we were drawing more warm humid air into the room. We bought a dehumidifier  which we just ran when the weather was warm which helped a lot. The problem disappeared in the winter. In the end we insulated the floor which raised the base temperature which cured the problem.

Probably not, I'm up in Shropshire and the humidity in my workshop, which is more or less the same as outside at this time of year, is 68% today.

But it all depends how cold the walls and floors are as to whether you get condensation or not,

As a cheap but effective test, you could try putting some plastic on the walls or floor; it needs to be firmly pressed down so that no air can get underneath. Leave it a day or so and see if water has formed on top or underneath. If its on top you have condensation if underneath you have damp.

There is an extractor fan in the kitchen (automatic type) and a manual extractor fan in the bathroom. We also leave the windows open weather permitting.
The strange thing is that we do not get any condensation on the windows, which I thought would happen if there was a condensation problem?

The ground outside is very water logged due to the property being built at the bottom of a woody mountain, so perhaps this is the cause?