Right, here's an update on the situation.
The pickup is wired to the neck vol pot, black & braid to pot, red to 1st tag with cap, green & white taped up & out of the way. Tapping the poles with a screwdriver gets a sound, but it's quite faint, as is playing.
I took the multimeter to the switch, as there was a signal from the pickup, but nothing from that pickup to the jack. I figured out that it wasn't the output from the switch, as the bridge pickup was working, and putting the multimeter on the output jack gave a 15k ohm reading, but if I switch to the neck pickup, there's hardly a reading. Took a wild guess at the problem being the wire from the pickup to the switch, so I've rewired that, (pups out, wire out, thread wire through, pups in etc, etc) and remade all the joints to the pot in the process, tested it, getting readings of around 7k ohm. Tried the tapping the poles again, and I could hear the tapping, but when I play, there is only a really, really faint signal being sent to the amp.
That was the situation last night, and I've not tried it today as I've just been too busy with other stuff. I'm kind of flummoxed now, so I'm going to leave it for a bit (and wait for any bright ideas from you lot! ;) ), if not, it's down to EMS for them to sort! :(