Hello and thank you for your question. I will be very pleased to assist you. I'm a practicing lawyer in England with over 10 years experience.
Has the work been completed please?
thank you. if the neighbours have commenced work without serving the appropriate party wall notice and your agreeing to the same or in default of which obtaining a party wall award, then it is possible for you to obtain an injunction to order them to cease any further work until such time as the above has been complied with. From what you say, they have voluntarily agreed to cease work and so on injunction may not be required. Once work is being completed, it is not possible to retrospectively applied for an injunction order for that work to be removed nor is it possible to retrospectively obtain a party wall agreement or award and so time is of the essence in respect of taking action in respect of works being carried out. In respect of such works that have yet to be completed, you can require your neighbour to serve upon you a party wall notice to enable you to appoint a surveyor. Certainly, you can contact a party wall surveyor to intervene under the provisions of section 10 the party Wall act irrespective of their failure to serve a notice
none of the above is of assistance in respect of any works they have already completed however...
In respect of any damage you discover that has been caused to your property which you reasonably believe was caused by the neighbours works carried out without a party wall notice, the case of Roadrunner Properties Limited v (1) John Dean (2) Suffolk and Essex Joinery Limited  EWCA Civ 1816 is material. This has provided more weight to the Act than the legislation itself affords. I this case a neighbour had reason to believe that damage had been caused by building works recently completed to the adjacent property, namely chasing into the wall using a heavy duty drilling tool. The case decided that the burden of proof would be reversed if the building party had failed to serve a notice and so the builder had to prove that the damage had not been caused by them rather than the normal situation where the claimant would have to reasonably prove the neighbour had caused the damage in order to claim.
Accordingly this places you in a strong position in relation to any damage you claim has been caused to your property as it is they that must disprove what you say rather than the normal position of you proving that they have caused such damage in relation to party wall works without notice.
If this is the case you can rely on the decision in relation to Roadrunner Properties and simply claim that the works have caused damage X Y and Z to your property. you do not have to produce any evidence of your claims the neighbours would have to disprove what you say as a consequence of the above decision therefore this places you in a very strong position in the event that you had to pursue a claim against the neighbours for future damage
Are you happy with the information I have provided to you above or is there anything above I can clarify for you any further?