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Water ingress over a period of time is not usually an insured risk which your own insurer would cover. We would need to examine the policy. If the landlord upstairs was aware of the issue there would be a claim against him for negligence in that because of his inaction he has caused damage to your property. That claim would not be made by your insurer on your behalf but by your solicitor on your behalf. You would need to raise court proceedings if a settlement cannot be made. I hope that helps. Please leave a positive rating so that I am credited by JustAnswer for helping you today.
Unless it is a sudden catastrophic event like a flood or a burst pipe you would not normally be covered and this seems to be a gradual event caused by lack of maintenance so the clam is against the other property owner.