'mmmm
I'd like you to make sure you know what the floors are made of. A house of that age could well have a leaking water main or other plumbing.
If the floors are wood, you can easily have a look underneath and a sniff for damp (yes, laminate flooring is hated by plumbers and electricians), you might even be able to hear a faint continuous hiss. If you have a water meter it will be easily detectable. Leaks are often under the kitchen or by the stopcock, where there are joints and elbows.
If the floors are concrete then it can be very wet and water can soak up into the building.
However a 1930's house really ought to have a DPC to stop water going up into the walls (it is fairly difficult to cause rising damp)
It is also possible that there might be a leak in your neighbour's house, and if they are higher than yours, it might be getting from the floor into the wall.
As you are on a hill it is also possible that water is running downhill, possibly from broken drains, and getting under the house.
If you can get recommendations for an experienced old plumber and a local builder who is familiar with houses like yours, they might be able to puzzle out the cause. Sometimes when you strip the paper off you can detect where the wettest patches are, and the source is often near there.
Damp-proofing will certainly not cure the cause.
BTW condensation, damp and mould in UK homes is usually caused by lack of ventilation and draping wet washing around the house or over radiators. You don't do that, do you?