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If water from their property is causing damage then the neighbour is liable.
They are liable for anything flowing from their property which is damaging yours.
It is a well established principle that you own the airspace above your land, so if your neighbour’s gutters overhang your land then they may be a trespass, even if you cannot reach them or they don’t interfere with the day to day use of your land.
If you have gutters in your airspace that have no right to be there, then it may be that you can insist on their removal. They are a trespass and, as a last resort, a court has the power to order an injunction to remove them.
A word of caution is necessary here, however: a gutter overhanging many feet up in the air may be considered by the court as a trivial trespass. Unless you can show some real harm or serious implication requiring its removal, then the court may not order its removal and can penalise parties for bringing trivial cases.
But in this case there is damage so they should be re-routed any water flowing away from your property
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