You’re doing the right thing.
I can’t believe the landlord / agent are not being helpful.
That is definitely rising damp / ingress and needs proper treatment with a chemical DPC and / or rectifying whatever influence from outside issues, possibly below ground level, broken drains, downpipe leaking, all manner of possibilities, not sure if you’ve noted any of these as I’ve not read the entire post of replies.
Worst case scenario it may need waterproofing with Newton 500 or similar and dry lined with, preferably, an insulated independent lining wall.
Give them notice to agree to arrange the work or do it yourself and withhold the rent until you have recouped the cost.
If there’s any dispute or uncertainty regarding the cause get a professional damp surveyor to inspect it and write a report.
Good luck, and sorry to hear you are in this situation.
Sorry David somehow this got mistakenly replied to your post, it was intended for the post below yours.
PS: The property is not conforming to housing standards and building control requirements of ventilation (10% of the room area) if the windows do not open, and as you noted no fire escape.