=from what you have said it does sound like your roof reaches over on to your neighbours property?
To be honest I believe the overhang on the gutter is into the shared boundary and has been that way since the property was built. I understand that it is normal for gutters etc to extend into the shared bounadry but you need perminssion to build walls into it.
I am not angling for an argument with my neibhour but I dont see why the wall need to be so close. It just makes it difficult to finish properly and I worry that it could result in damp in my walls.