If you are occupying the property under an assured shorthold tenancy the common ways of getting out is either by agreement with the landlord, or by you serving a notice to terminate in accordance with what notice period the tenancy requires (check the agreement for this term).
There is an outside chance that the tenancy contains a break clause entitling you to terminate before the end of the term. Again, you should check the tenancy agreement.
Wth respect to the disrepair of the shower, this does not automatically entitle you to terminate the tenancy purely on the strength of your opinion. If the Landlord does not repair it after you have asked you can carry out and pay for the repair works yourself and then write to the landlord asking them to reimburse you. If he does not you can issue a claim through www.moneyclaim.gov.uk for the money.
You may consider involving the environmental health officer of the local council, they will visit the property and if they deem the property to be unfit for human habitation (because of the shower) then they will serve an enforcement notice on the landlord. This will provide you with sufficient independent evidence that the Landlord's breach is serious enough to entitle you to terminate the tenancy.
You should check whether the tenancy agreement refers to the annex room, if it does then you can write to the landlord requesting a key to use it. In the letter you should refer to her previously stating she does not want to give it to you.
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