It may be first world problems but the difference for the neighbours is whether you can take things from the back of your house to the road or not and intrusion of rights. Many years ago I went through a similar thing when my neighbours wanted to fence off their land, preventing my access to the road from the back of my house. I'm glad that I did not allow myself to be bullied, took legal advice and forced them to recognise my right of way. It means that I do not have to haul garden waste, for example, through the house. My house is much more modest than these but the problem is the same.
Unfortunately if the new neighbours get away with it, others could use that as an example.