Aah, PartP!

Under Part P of the building regulations I think you need to get this
either approved by building control or installed by an approved
electrician; this requirement came into effect from 1/1/2005.

As I understand it, it is perfectly acceptable to do as you propose, ie
run armoured cable along a fence providing that it is protected from
damage ie:

1) Situated in a position where its not going to be exposed to
particular risk (reasonably high up on fence)

2) Properly secured using appropriate cleats (get these from B&Q or
electrical factors)

3) Where it comes out of the ground it should have some additional
mechanical protection such as a piece of plastic pipe to protect it
from spades and feet etc.

There are also requirements regarding the buried section regarding
depth, warning tape and/or protective tiles.

I'm not an electrician but installed several runs of armoured cable
before it became "unsafe" for me to do so; this reply is based on my
recollection of the regulations etc I researched at the time.