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Welcome to JA.
I am sorry to hear about your situation.
Please note that this is not a chat service therefore you may experience delays but rest assured that I will respond within 24 hours.
The Landlord and Tenants Act imposes a repairing obligation on the landlord and its likely your tenancy agreement imposes the same obligations too.
In view of the law and your current circumstances, I suggest you write to the estate agents and remind them of your rights under the law and the agreement. Notify them in the event the shower is not replaced or repaired within 7 days you will consider filing a complaint with the local council. Please note that the local council can step in to resolve such dispute by compelling the landlord to undertake proactive action to fix the issue.
Alternatively you can consider stating you will proceed to fix the shower if its not done within 14 days and seek to recover the costs from the landlord. Further you pitch the idea of deducting such costs from the rent.
I hope I have clarified the position, if not please let me know.
Thanks and stay safe.
You can but I don't think you will be successful at the moment given the time period the issue has been ongoing for and the landlord has taken some steps to fix the matter. Further the landlord could also state he is in middle of trying to sort the matter out.