Thanks for your question. Apologies it's taken a short while for anybody to reply.
It sounds to me like this is going to be a Party Wall etc. Act 1996 issue. Basically, if people wish to excavate and build within a certain distance (usually 3m) from a party wall (which is a wall which separates two lands), then they have to serve a formal notice to that effect.
If the notice is not served, then the person wishing to carry out the works cannot legally do this until the notice is actually served. An affected landowner (like yourself) might be able to obtain an injunction in such a case to stop the work proceeeding without the notice being served.
The effect of the notice is that it requires the parties to reach agreement on what works can be undertaken and how they're to be undertaken. If that agreement is not forthcoming, then the party serving the notice can ask for the appointment of a surveyor (who you must both agree - in default of agreement, you both appoint your own and he appoints one to resolve the conflict) who will determine what work needs to be done (or can be done) and how it is to be carried out.
You can get full details of the PWA processes and the law here: https://www.gov.uk/party-wall-etc-act-1996-guidance
OKay, then in that case, it's likely to be dealt with on common law principles.
In other words, you can do as you like with your wall and a failure to maintain it will not normally mean you're liable to your neighbours unless it causes damage to their land as a result. It might not be an appropriate wall for them to rely upon, and they have no right really to do this, and this is why in this kind of situation, you often see two layers of bricks forming the wll - one from each landowner.
Also, if it's your wall, they have no right to build on it or to tie into it without your consent. If they did, this would be trespass and you would be able to take action accordingly, either via a money claim for damages or an injunction to prevent them interfering with your property.
Potentially, you could be liable if this did damage their property as a result of it falling down. But that is going to be down to the law of negligence and nuisance, and I would question whether they, by building around a structure they know, or ought to know, was dangerous or at least wanting of maintenance, might have caused their own loss. That would mean your liability would be minimised or wiped out altogether, but you're right, there is the potential for you to be held liable.
As for pipes etc., in your land/airspace, you can ask for them to be removed if they trespass.
Planning is a separate issue, and is a public law matter, which if granted you'd need to consider arguments about their building interfering with yours somehow to be able to stand any chance of stopping it, or it being in breach of restrictive covenants, for example, which you have the benefit of. You should check your land registry deeds in this respect.