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Is this a ground floor flat? If not ignore but, if so - you could have some significant damp below the floorboards on that wall which is making the atmosphere around there very humid and also keeping the temperature low. Rising damp is mostly a bit of a myth (it can happen though) but damp brickwork lower down can certainly lead to damp plaster higher up, even if it's just due to it keeping the temperature low enough to cause a dew point.
Anyway as other have said, best to keep it well ventilated - can you get vents put in at the bottom of the wardrobe for example?
We have a built in wardrobe that just consisted of 3 sliding doors that are floor to almost full heightC top blocked off my a fake wooden ‘wall’ to make it boxed in.
When we moved in the old (think self made) wooden frame inside was moldy and the back wall was also moldy we ripped it all out, mold sprayed and cleaned the back wall, then during decoration gave the decorators good anti mold paint for the back wall
Then we instaled IKEA elvarli post mount shelving.
The mold has returned and taken over the back wall skirting board and taking out all the shoes at the back bottom of the wardrobe with it.
https://imgur.com/gallery/uqlhU1f
Images above,
Whats trademan do i need to properly solve this?
Likely outcomes, Replace skirting boards? clean skirting boards every month or two and keep nothing at floor level? Burn the flat down?
Everything above seems fine and the rest of the room isnt damp.
Wall is dry except for skirting board and the floor right by the skirting boards.
Its an external wall with no ventilation.
Edit:
https://imgur.com/gallery/Y62eshb
We had one of the cubord doors off the rails and up against the wall... and well, its bad behind that.
As soon as we reach the ‘proper room’ it all goes away, at least to the eye. It looks like maybe the skirting boards in this area are just up against raw wall, of some sort of gap? There doesnt appear to be plasted behind it