thank you. The information given by the seller's is in no way determinative and is simply information of what the previous owners believed or in some cases, an indication of past practice which in itself does not form legal precedent.
Responsibility for wall lies with the person on whose land it is built upon. Accordingly, if the wall is built entirely within the neighbours boundary, then it is the neighbours property and as such, responsibility to maintain. If a wall is built astride the boundary line then it constitutes a party wall under the party wall act and in those circumstances, responsibility is shared and in the event of a dispute, a party wall surveyor can be appointed.
Where it is unclear whether a wall is built entirely within a boundary or astride the boundary line or there is dispute on this point, then this May constitute a boundary dispute which you may or may not decide should be resolved through the land registry's boundary dispute service though from what you say, the does not presently appear to be a dispute as regards ***** ***** line or that the wall is built within the neighbours property.
if it is accepted that the wall is built within the neighbours Petit and as such it as their responsibility, it does not however follow that they must maintain the wall unless it can be shown to be dangerous. If you can demonstrate that the wall is dangerous then you can ask the local authority to intervene if necessary to serve an improvement notice to either remove or repair the wall but if it does not pose a danger, then in those circumstances it would be up to the owner of the wall to decide whether they wish to maintain it or not