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I didn’t think it was that sealed up TBH (based on the drafts from the doors etc), but the cold wall + fact the wet patches came up so quickly made me think it must be condensation - plus it seemed to be on the outside of the paper rather than looking like it was seeping from behind.
Yeah I’d not have expected the oven to do that, but wondered if maybe there is more moisture from a gas oven (which we had to put on full as it doesn’t seem as effective as the electric we’re used to).
I had wondered about just putting a decent extractor fan in the wall to see what happens - there’s a vent already in the wall pretty low down so we could try that without needing to change anything else, although placing isn’t ideal.
If the place is quite sealed up, get a dehumidifier and run it on high for a few days, see what happens. FWIW in our place - 1920s terrace - the internal humidity in the kitchen / ground floor is roughly aligned with the outside humidity, and that's with double glazing and the flooring pretty well sealed over. Does have working chimneys though...You can fight it with a dehumidifier but as soon as you shut it down it's back to doing what it's doing outside!
Seems curious that cooking in an oven can create enough humidity to do what you describe. Maybe if you had a load of pans on the boil with no lids? Condensation usually appears at the corners of windows, worth checking there too.
If this is simply the kitchen not being ventilated properly then it could be as simple as putting an extractor fan through the kitchen wall and venting the damp kitchen air outside. That's a builder / handyman job. A damp person won't want to suggest that because they'd rather sell products that appear specialist and carry low risk (to them) and high margins.
Opening the kitchen window when you cook will come a close second, but it's no help when it's pissing down outside and outside humidity > humidity in your kitchen.