Thanks for the replies.
FWIW, my guess would be that the noise IS related to the gearbox, but I'm just not sure if it's the common main-bearing fault.
The fact that it doesn't seem to make any noise when I pull away in 2nd made me wonder if it might be, say, the 1st gear synchromesh or something.
Although it sounds a bit like the noise of a dragging brake-pad, I'm pretty sure it's NOT the brakes because it only seems to happen when I'm accelerating (in 1st) and not at any other time.
Course, accelerating from a stop, in 1st gear, IS when the gearbox is under the biggest load so maybe it is the gearbox main bearings and what I'm hearing is the "first stage" of the problem.
Alternatively, I guess, it could the the bearings in the diff', which might explain why it's more obvious when I'm turning the steering wheel.
Bottom line, I'm afraid, is that if it IS a bearing anywhere in the gearbox/diff' I'm probably going to ignore it.
I only paid £150 for the car, as a cheap runaround, and I'm desperately short of money so spending £350 to repair the gearbox just isn't going to happen.
I lost my job at the end of March, I need a car to help me find a new job and I'll only be using the Jazz IF I can find work, at which point I'll be earning enough to replace the Jazz with a better car (or, if I decide it's worth it, repair the gearbox).