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2. I regret to say that just because the lifts in your tower block have not been working, this does not give you a right to withhold rent or to claim back rent from the landlord. I regret to say that the law does not recognise such a claim. However, I would advise you to negotiate with the landlord and see if they are amendable to making some deduction because of the difficulty caused by the lifts not working. However, just be aware that the law does not allow you to claim back rent. You effectively need to negotiate with your landlord and threaten to leave if some effort is not made to accommodate your wishes. So, seek to negotiate with the landlord but do realise that the law does not allow you to claim back rent for the lift not working in the communal areas.
3. If you require clarification or if there is additional information you wish to share, I will be happy to assist further in the resolution of your Question.
4. You are welcome. Glad to be of assistance.