Rights Over What is Believed to be a Party Wall Dividing Two Owners’ Gardens

Question

I have just bought a terraced house in Bristol. There is a wall running between my garden and my neighbour’s garden. The wall extends out of the wall of the (original) extension of their house. This wall then continues as the shared wall between our houses. I understand that the shared wall is definitely a party wall, but does it cease to be a party wall at the extension of their house, and then when it divides our gardens?
 
The wall is about 70cm high and the mortar has crumbled. It is leaning over dangerously (bricks have fallen off) and appears to run at an angle so it veers into my garden (i.e. if it wasn’t built on my land it has moved on to it). I doubt that it has foundations due to this movement, but can’t be sure. There is a fence on their side of the wall; the posts are on my side and there’s actually a gap between the fence and the wall, so in practicality it seems they are not claiming the wall.
 
I wish to demolish the wall as it is unsafe, particularly for my pets and the small children of visitors. I would then like to put a new fence on the boundary between our gardens (because I do not wish to claim their land and I want a higher fence).
 
Unfortunately I have been unable to contact the owner, which would clearly be the best way to resolve this.  I am unsure whether I should serve a party wall notice, assume the wall is mine (and demolish it), or assume the wall is theirs (and pursue some kind of action based on it being dangerous). Do you have any advice on whether this would be a party wall?

Answer 

The only way that you can tell whether the wall is shared (a ‘party fence wall’ under the Act) is by referring to the deeds of your property. There may be a plan attached to the deeds with some markings on it or failing that there may be a reference in the deed itself.

If it turns out to be a party wall you will have to serve notice under Section 2(2)(b) of the Act. You can get your neighbour’s contact details from the Land Registry.