OP,
With the best good will
"re-building their extension on the lawn were the wall once stood" is a confusing statement.
If they -
- knocked down a party garden wall without permission
- trespassed on your land without permission
- laid down foundations
- built part of the new wall on your side of the property boundary
- then you should state all this.
They either trespassed onto your land or they did not not.
Otherwise there is very little relevant information on which to offer advice.
Allow me to ask a few questions - the most basic first, then the more difficult and involved ones - these may or may not shed light on the situation.
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Have you ever spoken to your neighbours directly about this wall and extension?
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Where is the extension built that you can see the wall from your hall door?
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Why haven't you given said wall a lick of paint?
Was this lack of maintenance a result of a breakdown in relations between you both?
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While they built the wall, they also seem to have demolished a party wall.
Why wasn't ownership of part of this wall claimed by you and/or transferred to you after the fact?
Why haven't you given the wall a lick of paint recently to improve the saleability of your home - its allegedly on your property now?
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What exactly are you alleging your neighbours have done and what steps have you taken to remedy it in the meantime?
The normal course of action is to allege a breach of planning law has taken place and to request enforcement action.
This occurred "about ten years ago", and so may come under the remit of the Planning and Development Act 2000.
If this is so you had seven years to purse an enforcement action with this local authority.
If this does not come under the said act, you had five years to purse the matter with the local authority.
(i) Did the extension have benefit of permission and did it comply with the terms of the permission or not?
(ii) Did the extension rely on the Exempted Development Schedule and was it built within its strict requirements or not?
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Are you alleging trespass occurred without consent and that this compromised the planning permission or the work carried out as part of exempted development?
Did you write to your neighbors and the local authority alleging such trespass took place and requesting regularization under the planning acts and compensation or requesting demolition of the portion built on your property and reinstatement.
Was there an enforcement file opened in relation to the development and what was the outcome of the investigation?
Is it still ongoing?
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In relation to the history of events, why were you away from a property for a year - is this an investment property or a sole domicile?
If you knew you were going to be away for so long, why was there no-one keeping and eye on the property for you and alerting you to the works?
Surely you had a key-holder in place in case of a fire emergency or whatever and they were able to contact you.
You cannot build a significant extension in a weekend.
If someone did alert you, why did you not retain the services of a competent architect and or engineer to monitor the works and report back to you, having informed the neighbours that they would be fully liable for their fees?
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Apologies if this seems like a deluge, but these are just some of the questions arising in this instance.
I look forward to reading your responses.
ONQ.
[broken link removed]
All advice on AAM is remote from the situation and cannot be relied upon as a defence or support - in and of itself - should legal action be taken.
Competent legal and building professionals should be asked to advise in Real Life with rights to inspect and issue reports on the matters at hand.