Party Wall agreement never sought?

check with your insurance if you are covered for some legal guidance first off then take it from here.
The builder is at fault for carrying out this work as there is no way this is the correct way of doing such a job, but the buck stops with the owner of the neighbouring property so any approach should be aimed at them.

Have a look at the plans online that the neighbours must have submitted with the Council - look at the detail. If the work has gone against Planning requirements then Building Control should have not signed this off anyway. A call to the Council may assist and they may point you in the right direction themselves especially if there is something which is a danger right now. Good Luck.

This is not a case of trespass. Your neighbours, not the builder, are responsible for observing their statutory duties under Party Wall Act. You may suffer damage as a result of their work, and they will need to prove they haven't caused it. But without a Schedule of Condition to compare conditions before and after, it will be nigh on impossible for them to identify what damage has been caused by their works. Not that you would, I'm sure, but you could make spurious claims for pre-existing defects.

If you then take your neighbour to court, because there has been a breach of statutory duty, the court is likely to reverse the burden of proof, which means your claim is assumed to be correct unless your neighbour can prove otherwise. They may therefore be ordered to pay for any number of repairs, which in reality are not their responsibility (plus solicitor’s and court costs).

It sounds like your relationship with your neighbours is gone, so threatening legal action is no loss.

Did you not raise the matter before the work was complete? You may have had a duty to mitigate your loss.

Reply to the comment left by Terence Joseph at 22/02/2021 - 14:18
Builders can be a real pain in this matter. They will have taken the job, have a schedule to meet, and need to be paid ASAP. Probably other jobs lined up too. So they cannot be delayed, possibly by 2 months, by something as 'trivial' as a Party Wall Award, so they will conveniently avoid discussing it with their client, who may not know what their obligations under the Act are. I've been through a few Party Wall Awards, one of which was horrendous. The onus is on the party having the work done to fulfil their statutory duties under the Act, not the builder. Building Regs and Planning don't come into it, unless the work being done breaches Building Regs. Yes, they can build on the boundary and use your wall (is it within your side of the boundary?) but they must serve notice on you BEFORE starting work and you must agree to the work, and if you don't, employ a Party Wall Surveyor to act 'for the party wall'. You could have served an injunction on your neighbours during the work and they would have had to stop until resolved. However, I believe you can still seek damages after the event if you really do feel they have compromised your amenity, and to be honest, they don't have much of a leg to stand on. They could be forced to remove their works, make good your property, and pay your costs! You need to decide if it's really worth the hassle. Regardless, you should get something in place with them which recognises their responsibilities for any future damage to your property.