Tenant rights to give notice within a contract

Tax Planning and Financial

hi,
if a tenant has signed a shorthold tenancy agreement for a 12 month period, and they subsequently find that the property they are renting has mould and damp, and they want to give notice and move out, what is the position from a legal point of view .. i.e. is there a standard notice to quit period that applies even though the landlord has not mentioned notice periods in the agreement, and although he has issued a 12 month period rather than the usual six?
Also, what else can they do if they cannot move out? - they have tried to get the landlord to fix the problem, but he has failed to rectify it after two attempts. They have mushrooms under their sink, surely that have some rights?