Thanks for the replies guys. I desoldered the pickup earlier today and tested it with the multimeter - 13.8K, which is pretty much as expected. I had the idea while I was there to wire the hot directly to the output jack wire as Toe-Knee suggested, and when I plugged it in it sounded great! So I wired it back up to the volume pot and it still sounded great!? It seems that in desoldering a couple of joints and remaking them the problem was cured. I guess it was just one of those things.
Anyway, I'm happy now, I've been playing it non-stop since :)
One thing I did notice, was that the output is ever so slightly greater when the pickup was wired directly to the jack socket - not a big difference, but noticeable. Is this normal, or does it mean I have a poor quality pot or something? I was actually considering just leaving the pickup soldered directly to the jack socket permanently :lol: but I need my volume pot.