Issues with neighbours over wall !!

I live in a row of terraced houses, I am the second last house from the end, the end of terrace house differs from the rest, it is bigger and facing out (kinda perpendicular to my house). Their garden is to the side and my garden is running alongside this to the back of my house. As their house is wider the back wall of his house is in my garden and then the usual timber fence makes up the rest of the boundary between the gardens. My question is what rights do I have to this wall, the wall is the back wall of his house but it would be my boundary wall also? They would have no access whatsoever to the back wall of their house without coming through my garden (my house is a mid terrace so no side access).

The guy next door has taken exception to me erecting a clothes line that joins on to the back of his house and also sky digital have erected a sky dish to the corner of my house (the bracket is on my wall) but he wants both moved as he says this is the wall of his house. Now the sky dish is on my wall, doesnt touch his wall at all, doesnt overhang into his garden and doesnt block any views as there are no windows at the back of his house! The clothes line is one of those retractable types and is attached to the wall at the back of his house so that it can run across my garden. I am arranging to have both the dish and clothes line moved for peace sake! Not sure how he even noticed as to see both he would have had to hang over the garden fence as neither are visible from his house or garden! But I was wondering can anyone tell me what rights I have to this wall - even if this guy wants to paint this wall he would have to access my garden. Is this not a jointly owned wall?

Correct me if I am wrong, but isn't this a party wall, meaning you can do whatever you like to it on your side and he can't object?
Check with the developer if a new build and they can tell you, but don`t move anything until confirmed