Gordon1111 wrote:
I'm looking to build a fence between a neighbours wall and the side of
my house.

Parallel with the wall? So you have two boundary features, the
existing wall and a new fence alongside it? Changing from:

|
house |------------
|
to
|
house |============
|

The fence will only 1.3mt wide,

millitons? Or do you mean metres - 1.3m ? And do you actually mean
1.3m /long/ ? A 1.3m wide fence is a shed.

The only fear i have is that i may get noise / vibration coming
through the fence into the house (living room is next to it), from
my neighbours gate slamming or kids kicking the ball against it.

On which side is the height difference? Is your land lower than
your neightbour's or higher? I'm finding it hard to picture your
neightbour's brats kicking a football past the existing wall and
across the height difference to hit the fence.

JGH