OP, you mention your NDN’s plans as extending up to the shared boundary. As others have mentioned a party wall survey will be needed for work attached to your property. You should get your own surveyor, your NDN will no doubt suggest you use theirs. Don’t, the surveyor is working for and being paid by your NDN so will work towards their interests. Appoint your own, your NDN has to pay for this.
With regards to the boundary between you which is not building, is this fence or wall and who is responsible for it? If your NDN is building along the boundary and assume this is into their back garden this will involve taking down the fence/wall. You say you have DC, how is this going to be managed for their safety and enjoyment of your own garden? Have you any structures, greenhouse, shed, or established plants your side that will be affected? Builders are very fond of ripping the whole fence/wall down so they have lots of access (and use neighbours garden as a work area given half the chance).
You can say you want a fence of some sort put up for your privacy and security or even better they have to build from their side leaving the boundary fence/wall in place.
Your NDNs will bellyache about the extra cost involved. Ignore them. Anyone undertaking this sort of work should be budgeting for party wall surveyors and fencing. If you can insist they build from their side it will take them longer however so noise for longer (and oh dear will cost them more as well)
Re the noise: your Council website will have details of the permitted times this is allowed. 8-6 weekdays, 8-1 Saturdays and not at all Sundays and bank holidays. This is only outside building noise so they will be able to do things inside though.
If you appoint a party wall surveyor this will all be laid out in letter form and sent to your NDN and their surveyor. Your surveyor will come and inspect before, during and after the work is done. This should keep things neutral as best you can with your NDN.