You say it's a screened cable; if you can recognise it as that you sound a
bit technically with it as might be your neighbour. Do you know if it's low
voltage lighting? If it is, you're on a sticky wicket from the technical
side because it will be isolated from the mains.

Even so, it might be a good thing to have a word with the electricity
suppliers or perhaps check the latest IEME Reg's in your local library.
It's a long time since I read the regulations which always keep abreast of
the times, so there's bound to be something about extension cables,
(screening may not be enough- perhaps they should be armoured), isolation
transformers, earth bonding and maybe official sactioning. You could have a
field day if the extension is just that from a 13 amp socket!

Of course, you could always paint the cable the same colour as the fence; it
would then be less unsightly.

Regards

Ron