Just to play Devil's Advocate, with regards to your worries over your electronics...
most reputable contractors are bonded and insured. So, if something did get broken, or went missing during the job, they would generally be liable for repairing/replacing the item.
If you do end up letting them access your flat, I would think it perfectly reasonable if you requested verification of the contractor's insurance, etc. And, regardless of whether anyone's in and out of your flat, it's always a good idea to keep an up-to-date inventory of those types of belongings, for your own use in case of a break-in or insurance claim.
To be quite honest, other than a bit of inconvenience (and, in my experience, decent contractors are also quite good about cleaning up after themselves, and the person ordering the work should insist upon this), I'm not sure what you have to lose by allowing the work. You're certainly free to argue it with your neighbor and/or landlord, but it just seems like it might be a lot of worry, inconvenience and melodrama over not much.