google wrote:
not much work involved in connecting an earth cable from my flat to
the box (3 meters).

Here is where spelling is very very important.
meter - the thing with spinning dials that measures how much leccy
you've used
metre - a unit of distance being approximately 39 inches.

Looking at the picture it looks like the supply supplies an earth,
there's a black, red and green coming in from the bottom; the red
going to a set of fuse heads, the black to a common block, and the
green to an earth tag, then all three continuing upwards; with
consumer read+blacks going off to the sides.

It looks like your neighbour has connected their earth to the
case, not to the earth tag, and is relying on the case providing
an electrically sound connection to the earth tag. Earths really
need to be made to a single connection and not rely on intervening
metalwork for their connection.

JGH