The whole balance of enforcement of this law is wrong, the council doesn't regulate this, so the poor householder next door to the building work has to act as surveyor, lawyer and snoop to gain anything from law. Protect the public don't dump this kind of technical regulatory enforcement on them.
Your neighbour is doing something in their house, they won't tell you what it is, they have submitted plans to the council for building control, but they won't tell what your neighbour is doing either. You suspect your neighbour may need a party wall agreement for the work, but they haven't offered you for one. You are now compelled sit there while work continues without an agreement or engage a surveyor at around £1500 to intervene on the assumption you may need a party wall agreement, which is both a financial risk and a declaration of war on your neighbour.
Why not ensure that building control and planning permission will not be issued without the correct Party Wall agreements in place, that way the neighbours a protected as of right not the good graces of the people carrying out the work.