It's a mystery that's got everybody scratching their heads

Is there a second joist under the boards there along the one we can see?

Mr. HandyAndy - Really

 

As others have said you will have to lift the boards. Just cut through in the middle of a joist say at least a metre from the wet ends after removing the nails. Then put some newspaper down and see if that gets wet. If it doesn't you are in the realms of the supernatural! Carry on investigating until you find the source.
As the room was very wet initially which you have mainly eradicated IMHO it is probably coming up from the ground and would be worse near a fireplace.
Our house is about the same age as yours and was built on brick foundations on clay (even though the Romans had concrete). The clay was less than a foot under the floorboards. Having had a poor survey we found that the joists had rotted completely under the stairs and there was a lake under the house and we had a concrete floor fitted 30 years ago and no problems since.

In your case water is entering the boards through the end grain and is passing between them by capillary action.
IMHO it must be coming up from below from saturated ground.

KIAB Sorry to go over old ground but it is a bit infuriating as if any of us were there and had cart blanche to rip the place apart I am sure we would find the source of the water/damp. No disrespect intended to OP.

 

Well as said the way forward is to remove one board stick it somewhere else and see it dry out. Then lay a bit of batten in the same position not touching the other boards and see what happens.

Certainly a puzzle maybe;

1, you have a pet, small child or adult that is not house trained.

2, As suggested demonic possession but I my experience it is usually blood not water.

3, I wonder if it is some sort of process like plaster salts where a damp course is replaced but you have to strip the plaster because it has taken to absorbing moisture, I had a plasterboard ceiling where a patch from an old leak kept giving damp readings despite there being no leaks etc.

Still, it sounds as if your damp tester is having a great time with it's orgasms anyway!

 

Thanks for the update, we will see what happens next.
So, you have used new floorboards...

 

Well at least that's moisture resistant.

 

Hi
Wow this looks like a problem I had a few years ago turned out to be an under ground water run from an old drainage pipe that house was built on was covered in a flagstone and water was running underneath soaking in on underside and then transferring to top of joist eventually had to dig floor up and put a waterproof membrane (not plastic looked like fibreglass) in place and then cover with dry mix before relaying concrete floor

 

Sorry just read rest of thread looks like it's sorted without all the hassle

 

Intrigued by this and I wonder if there is a drawhole under the hearth and opposite an airbrick in the outside wall?

What used to happen was that builders would put a drawhole to get a good draught under the flooring and up the fire's flue to circulate air. Then along came insulation and BCO and drawholes were partially or completely blocked. The result was a build up of damp and moisture.

Alternatively warm moist air could be drawn in through the airbricks and manifesting itself as damp on the flooring.

As I said inrtriguing and no doubt man made. Ghosts, bah humbug.