thank you. the circumstances you describe give rise to a potential claim in something known as "Tort". I'm not certain if you have come across this word or not but even if not, you will know what it is in that it is the law that underpins claims such as personal injury claims, car accidents and so on. Essentially, wherever there is a situation where there is no contract between parties but damage has been caused, any claim in the circumstances would typically be founded in Tort.
In order to succeed with the claim in tort, you need to be able to show that another party owes you a duty of care, that the party fell short in that duty (were negligent) and that as a consequence of that negligence, you suffered damage to yourself or your property.
To translate that into the practical circumstances you find yourself in, you both occupy neighbouring flats and as such, you owe a duty of care to each other both in tort and under the terms of your respective lease agreements. Accordingly the first requirement is satisfied.
As regards ***** ***** there would be no claim available against neighbour where there is been a leak on the first instance of that leak in the assumption that the owner had no prior knowledge of the issue. In other words, it is simply an accident or at least the is no negligence on the part of the neighbour. however, on the subsequent occurrence of the same leak, negligence is much more straightforward to imply because an argument can be raised at the proper work required to repair the leak occurred on the first occasion was not carried out whether this be deliberately or more likely because they have not paid to have the necessary investigation carried out. A third instance makes it easier still to imply negligence for the same reasons.
accordingly, in the circumstances you describe, you would have the basis for what would likely be relatively strong claim for negligence on the part of the neighbour and therefore costs in respect of the damage the leak has caused. If your maintain a legal cover with your insurer, it may be that your contents insurer would be able to assist you in this respect. Otherwise you can bring a claim yourself if necessary.
Obviously, I am not suggesting that you launch straight into legal proceedings with neighbour is clearly there is the question of neighbourly relations to consider, but clearly in some way, the leak needs to be addressed and so you may at least need to consider gently surely raising the issue that the damage to your property is getting worse there will be a point where you will need to consider your options in this respect and perhaps ask if they have insurance for third party liability.
ultimately, though I am certain you would wish to escalate slowly in this respect, your default position is to issue proceedings in the County Court using the following link:
You will need evidence of the damage you refer to and an estimate of repair costs which may require you to ask a contractor who is a plumber and decorator or subcontractors to provide you with a simple report and quotation in this respect.