Apart from the EH involvement above, the other suggestion is the hire of An industrial dehumidifier. These things are the size of a small refrigerator, and from what you say you will get couple of litres per day out of them. Question is, who pays. Obviously not you but either your landlord or maybe social services.
It sounds like your landlord is fobbing you off. Solving damp issues in old houses is never simple and it may be coming from a number of sources - ground, leaking gutter s and so on.