Thanks for the replies chaps - too late & internet is too slow to answer them all individually now, so I'll do a couple:
Anthony - as far as I am aware, the chuck is mounted OK. I've not disturbed it since I bought the lathe a few months ago. I've not checked the runout on the chuck body, will do that tomorrow. However, the work hasn't been moved since I took that cut, so I can't see how the chuck would cause a taper? Even if it's mounted cockeyed, surely the lathe would cut what seemed to it to be a perfect cylinder - it'd only be when you compared that to the ends (or previously turned work) that the lack of concentricity/angle would show up?
I've only checked with the DTI on the top of the work so far, it may be that there's wear in the bed causing the saddle to drop. A long test bar ought to show this. I think I have enough kit here to actually turn between centres now, so maybe that's something to try. But not before....
...Andy - thanks for the Rollie's Dad Method reference; first link was a PDF which explains it in nice clear terms. I didn't immediately "get" why it works, but I see it now. I'll try that first, before I go putting drive plates on the lathe, etc..
I see you also answered, in better terms than I, why I don't think it's the chuck at fault...