I will try to assist you with this.
If you are not prepared to grant access to your side for this wall to be rebuilt, how would they be able to facilitate the build and for example carry out the pointing of the brickwork to make it look acceptable? Or are you now not bothered about it being done?
The situation under the Access to Neighbouring Land Act is that you must grant access for any work required to preserve a property. That means to maintain it. It does not allow for new building.
Under the Party Wall Act anyone who was building up to the line of junction is allowed access to the neighbouring land to facilitate the build which is the situation that you were originally in.
At present this is neither preserving the property nor a new build and it would be for the court to decide which, if any, Act applied here.
There is actually no reason why the whole build could not be carried out from one side but it is highly likely that what you would then be faced with looking at could look a mess as the builders may not be able to finish it properly and you may be shooting yourself in the foot by not allowing access to facilitate this build. If you are happy to continue to look at the wooden fence the local authority are unlikely to try to force you to grant access unless they were adamant that this must be replaced with redbrick and they decided to have the court determine the matter under one of the statutory provisions. It is unlikely but possible.
What you have to decide of course is whether you are happy with the fence and want things to stay as they are or not.
Can I clarify anything for you?
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Unfortunately, the Party Wall Act has no sanction for failing to give notice under the Act. The only remedy under the Act is to stop the build partway through by applying for an injunction. As such, that Act is no longer relevant. You should have done is apply to court at the time for an injunction to stop the build as soon as it started pending a Party Wall Award (agreement).
I accept that he did not apply for planning permission but as soon as he started to build, you could have applied to court for that injunction.
As the only persons who would be affected by the material of the adjoining wall would be you and your wife it is most unlikely that the council would insist that the adjacent wall is rebuilt. Nonetheless, they are entitled to insist that it’s rebuilt regardless of any objections by you or your neighbour.
In my earlier answer I said this is where the court would have to decide whether he was allowed access under the Party Wall Act as this is a new build their whether he was allowed access under the Access to Neighbouring Land Act for maintenance of the property. It could well be that the court decides not either.
If the court did grant him access, then he would be responsible for reinstatement and any damage.
At this stage in time, I wouldn’t do anything either. I would wait to see whether the council or the neighbour threaten application to court to compel you to give access and at that stage, I would deal with it. If you have house insurances, check to see if there is a legal expenses cover that would pay for the legal costs of defending any action brought by the neighbour or the council.