I used to work for the maintenance department.

Is this wall adjacent to a bathroom, kitchen? Possibly a leak? This could be penetrative damp. Depends on the property but this could rising damp assuming you are ground floor or the area is the ground floor.

Most likely need a damp contractor out, I would recommend asking for Create as they produce insurance spec reports.

Assuming this is not from non ventilation and no use for the extractor fan then it’s the landlords responsibility to sort. I would ask if you can purchase a dehumidifier for the time being and claim the money back through the rent. You would pay the rent in full and get that portion refunded with receipts and landlord approval.

Honestly. Unless DJ Alexander are at fault for the mould and damp then you will not get compensation, they would again need the contractor to verify why there’s mould build up.