Unique party wall confusion

slinkymassive

I am trying to find out exactly what party wall section I need to notify my neighbours about. I am building a single storey extension, solely on my land to the legal constraints, so does not require planning permission.

I live in a terrace house, but they are built in a U shape with me being in the center. The houses are not flush and their walls make up the boundary of my garden.

I originally asked both neighbours if I could use their walls to save me from building another wall inside my boundary ( lean to), but they do want me to use any part of their walls. So that leaves me with building a wall inside, close to their existing wall (around 6 inches). So is this an adjacent excavation notice or a line of junction notice?

Any advice would be appreciated.
I cant post a link for a picture on here but have one if that helps