What do I do about damp?
The first thing to identify is the exact nature of your problem - is it damp or condensation? The second consideration is who has the responsibility for solving the problem?
Damp is caused by a defect in the property - moisture entering the property from outside. This is often ndicated by white crystals on the plaster at the edge of the damp patch. A defect in the structure of the property would be the landlords responsibility, with one major exception. If the dampness is caused by a lack of damp course, instead of a defective damp course, then there is no obligation upon the landlord to install one.
However, if there is a defect that your landlord won't repair, you should follow the advice on the repairs page.
Other than a defect in the property, any 'damp' is more likely to be caused by condensation - especially if the 'damp' is accompanied by black mould/mildew. Condensation is the responsibility of tenants. It is caused by the tenants lifestyle, moisture in the air created by laundry, bathing, cooking or even breathing. If this moisture can not escape from the property it will condense on cold surfaces, in particuar those with limited airflow.
Aberystwyth University have produced an excellent guide to reduce the effects of condensation / mould in rented properties at http://www.aber.ac.uk/residential/en/accommodation/condensation-eng.pdf