In message , Tim Lamb
writes
Presumably the armouring will have been connected to whatever junction
box was used at the original load end by the securing gland.

If such a junction box were metal, it should give a good earth
connection..... I think you need some current flowing at 50HZ to
energize a cable finder.

Just some notes on this and earlier comments...

At least one of the boxes will need replacing, and there are visible
problems with one of the securing glands. I believe all the armouring is
still earthed though.
The main armoured cables are definitely coded red, blue, white and one
box has 2 whites earthed to the box. The third white in the same box is
tested live.
There is a bit of a family dispute (long distance at the moment) about
what to do next. I think we need to disconnect and measure until we
understand exactly what each individual wire does and which direction
the power goes. Son thinks we just have to find a way to trace the cable
until we find the underground junction box that he thinks must be there.

Anyway, I have invested a small amount in a pre-loved metal detector on
ebay and will practise with it before he arrives back at the weekend. I
don't really expect it to work. It may have to detect cable under crazy
paving.

Running a new armoured cable on the surface tucked in at the base of
walls would be possible, but the amount of gardening work involved is
daunting and a couple of paths would have to be crossed.
--
Bill