It would seem we have a misunderstanding how the Party Wall Act procedures work.
If the building owner carrying out the work finds themselves in a dissent situation they have to pay the costs of the adjoining owner's or the agreed shared surveyor. That is one of the reasons the Act was implemented, to protect adjoining property owners from potentially unscrupulous or negligent building owners, cowboy builders, dodgy property developers etc.
Unless the adjoining owner does something very silly it will never cost them a penny to have professional representation of an experienced party wall surveyor (never use a solicitor). It can cost the building owner a fortune if they fail to consult the neighbours and make sure they are going to agree to the work.
It is how the OP described their situation. They don't want to stop the work they just want to make sure there will not be any damage to their property. The neighbour here should be talking to the OP to reassure them and arranging a schedule of condition to agree any remedial works at the end of the job. Something they could work out between themselves for free as neighbours should. As it is they are being uncooperative so they are potentially working this up to a full blown Party Wall Award that will probably cost them £2k. It will not cost the OP as adjoining owner a single penny. The neighbour is being very foolish and not very neighbourly.
If the building owner carrying out the work finds themselves in a dissent situation they have to pay the costs of the adjoining owner's or the agreed shared surveyor. That is one of the reasons the Act was implemented, to protect adjoining property owners from potentially unscrupulous or negligent building owners, cowboy builders, dodgy property developers etc.
Unless the adjoining owner does something very silly it will never cost them a penny to have professional representation of an experienced party wall surveyor (never use a solicitor). It can cost the building owner a fortune if they fail to consult the neighbours and make sure they are going to agree to the work.
It is how the OP described their situation. They don't want to stop the work they just want to make sure there will not be any damage to their property. The neighbour here should be talking to the OP to reassure them and arranging a schedule of condition to agree any remedial works at the end of the job. Something they could work out between themselves for free as neighbours should. As it is they are being uncooperative so they are potentially working this up to a full blown Party Wall Award that will probably cost them £2k. It will not cost the OP as adjoining owner a single penny. The neighbour is being very foolish and not very neighbourly.