Thanks for your question.
I'm afraid you will be bound by the AST unless the state of the property is so bad that it is unfit for human habitation.
If the state of repair (particularly damp) is very bad then you should contact the local authority environmental health department and ask them to send an officer round. If the state of the property is bad he will issue an enforcement notice against the Landlord to carry out works and this may prompt him in to making the repair. If he finds it unfit for human habitation then he will declare it as such and you will be able to terminate your agreement with the landlord on the basis of this breach, be sure to get written proof from the department that the find it uninhabitable.
I note you think it will cost a lot of money but you have a right to a property in repair under your tenancy agreement. You should formally write to the the Landlord & Agent (address it to both) specifying the disrepair, making a list of the reasonable repairs required and ask that they make those repairs within a reasonable time (eg. 7 or ten day). you should state that if the landlord does not make the repair within that time she will pay to have the repairs made and will seek to claim the expense from him and are prepared to make an application to court if necessary (use this initially as a scare tactic).
If the landlord does not make the repair you can pay to have it done and then write formally again to him and the agent requesting the payment of the cost within 7 days. If the Landlord does not pay you can issue a claim for the money yourself through Her Majesty Courts Service's online service: http://www.moneyclaim.gov.uk/
All deposit under ASTs have to be placed in a tenancy deposit scheme within 14 days from the date of the tenancy and you can sue the landlord for the return of the deposit and a fine of three times the amount (payable to her) of the deposit if it has not been placed in a TDS. You may consider seeing how your other efforts go and keep this line of enquiry back to use as leverage later if they have not placed it in a scheme. Any agent/landlord worth their salt would have placed it but I thought you should know just in case.
If you start making noise in the above ways then the landlord may decide that he would rather just release you from the tenancy early, either that or he will carry out the repair works.
Its pretty cheap and straightforward to use.