Thank you. If the guttering is attached to her house then I regret the guttering is almost certainly her responsibility I am afraid. The reason I make this statement is two fold:
1) because the guttering is attached to her dwelling the presumption is that it belongs to her and is therefore her responsbility to maintain - it does not matter that the guttering is overhanging someone elses property. The fact it is overhanging may be an unlawful trespass but since this is not being raised I will leave that issue there unles you would like me to do otherwise;
2) if she could prove that someone had attached the guttering to her property without her permission - this would not be straightforward as the assumption would be that it was the builders of the property or contractors employed by her unless she can prove otherwise - then of course she could require that it is removed and refuse to maintain it as you suggest. However then there is the issue that she would be unlawfully draining onto the neighbours property water from her roof without a legal easement (right) to do so. Therefore even proving the above as a means to avoid responsibility for maintaining the guttering is likely to give rise to this further problem when she could potentially be required to cease and desist tdrainging her roof water onto the neighbours land.
It would be worth checking your mothers deeds to ascertain if she does have any rights to overhang the neighbours proeprty or any right of access. If not it is possible to obtain an order under the Acces to Neighbouring Lands Act for an order for access to the neighbours property but I would not anticipate this would be necessary because it is likely that the neighbour will be more exercised in practice regarding maintenance of the guttering than your mother so I would imagine the neigbour would afford access for maintenance without quibble.
Of course notwithstanding the above, there is nothing to prevent you mother agreeing to share costs or otherwise in respect of the guttering. he neigbour could potentially seek an order against your mother forcing her to maintain the same but the costs would likely outweight doing the work himself so it is unlikely to develop into a full blown dispute.
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