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Good evening, welcome to just answer I am a solicitor and reviewing your question now for you.
If there has been damage to the building as a result of the fire from neighbour property your landlord should be pursuing them for compensation. If they did not have insurance then it’s for them to meet the cost personally. Your landlord has responsibility to ensure your rented property is not in disrepair and if it’s a health and safety issue you must report to the council. Any clarification please do not hesitate to send your follow up question, I am glad to clarify. All the best.
Good morning, if you have suffered any loss that you can quantify you can claim from your landlord, whether they look to their neighbour or their insurer for indemnity cover would be irrelevant to your claim.