You could line the inside of the loft with something nailing it to the rafters from below but the landlord might get upset and you may well disturb the ventilation in the loft. Many houses have no roofing felt at all. See this...
http://www.buildingconservation.com/articles/pdf_roofsbreathe/roofsbreathe.pdf
Dampness in the bedrooms is unlikely to be due to the decaying felt in the loft space. In the winter the walls and windows are cold and the air in the house is warm and carries plenty of moisture - the result is condensation on the cold surfaces.
You might consider a Dehumidifier (Argos do one for £50) but can help yourself by keeping doors closed especially kitchen and bathroom - opening windows when cooking and bathing - providing some ventilation during warmer days to air the bedrooms and possibly turning the heating down a bit especially in the damp rooms.
Peccavi
December 2008