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Hello and thank you for your question. I will be very pleased to assist you. I'm a practicing lawyer in England with over 10 years experience.
Do you have evidence of his acceptance of liability please in writing?
The starting point for this is that if the accident was caused by a high wind or gale as opposed to some fault or negligence of the landlord - e.g. failing to secure something properly - then the landlord is not liable in law for any of the damage caused and accordingly anything he agrees to pay for is entirely voluntary on his part.
If however he is at fault in some way as above then he is liable for the damage caused and it follows that you make a claim for all reasonable losses so far as you cannot mitigate them which may include car rental if you need a replacement car for work etc
If you had confirmation of his acceptance of liability then you could seek a claim for the above. You be able to obtain written acknowledgement of liability from him? If you cannot you would need to show on the balance of probability some fault on the part of the builder in order to make a claim.
If you do not believe you can do so then a claim for the rental car may be difficult though your own insurance cover may incude a rental car provision you could potentially claim against.
Is there anything above I can clarify for you any further?
If I can assist any further as the situation develops please do no hesitate to let me know.