This is the least comfortable page on the site and it is worth being straight about it. The Act works forwards: notice, reply, award, work. Once work has begun without any of that, the machinery the Act provides is not available in the same way, and the answer is a mixture of practical steps you should take today and legal ones that are not this site's to give. What follows is the first half, plainly, and where the second half belongs.
Record the property today, before anything else
Photograph every room on your side nearest the work, and every elevation facing it, in daylight, at full size, with the date. Note what already exists: cracks, sticking doors, lifted tiles. This is a schedule of condition made late, and a late one is worth far more than none, because the argument that follows will be about what changed and when. Do it before you write to anybody, because once a letter has gone the neighbour may hurry, and a record taken after that proves less.
Write, once, and keep it factual
A short letter saying what you have observed, that you have not received a notice under the Party Wall etc. Act 1996, and that you would like the work stopped until the position is regularised. Keep a copy and the date. Many jobs come back on the rails at this point, because the building owner did not know they owed a notice, and a notice served now still runs its period from now. There is no retrospective party wall agreement: a notice cannot reach backwards over work already done.
Where the rest of it belongs
Once work has started without notice, the remedies are through the courts rather than through an award: an injunction to stop the work, and a claim for damage. That is a solicitor's job and not a surveyor's, and it is not something this site advises on. The related question, can neighbour refuse party wall agreement, has a clear answer that helps here: an adjoining owner cannot veto notifiable work, only dissent to it, which puts surveyors and an award in place. That is what should have happened.
Questions people ask about neighbour started work without party wall agreement
Construction next door my rights uk, in one line?
To be served notice before notifiable work starts, to have a surveyor appointed if you dissent or say nothing, to a schedule of condition, and to compensation for damage caused by the work.
Can I stop the work myself?
Not by standing in front of it. Stopping work is an injunction, which is a court remedy and a solicitor's advice. What you can do today is record the property and write once, factually.
Does no party wall agreement mean the work is illegal?
It means the building owner has no authority under the Act for work to the shared structure, and none of the Act's protections. Whether anything follows is a legal question, not one this site answers.