Hi Gander0,
There is a procedure to follow in the Party Wall etc Act 1996. The act isn't invoked unless you have served formal notices of your proposed works so whilst they may have signed a contract with their surveyor he/she is not yet appointed under the PWeA.
Side returns are not generally complicated (if no basements exist or unusual/unsafe structures are involved) and shouldn't need more than an Agreed Surveyor (one surveyor acting for both parties) to draw up an award.
Your neighbour needs to consider that only reasonable fees are due (it is not a licence to print money). They too must mitigate expenses or they may find themselves having to pay excess fees over and above what is a reasonable sum of money for the work executed in the event they demand you use their more expensive surveyor without good reason. I would certainly consider demanding fee scales from neighbours surveyor in advance of serving any Notices so as to make them aware you intend to monitor such things closely.
There are quite a few concerns about PW surveyors on here so my advice is to go to someone local and make sure the notices you serve are valid.
Try Jeremy Clarke (MRICS) at
www.SWLondonPartywalls.co.uk. 020 38 58 78 88.