Thanks, D.
After much muttering and spluttering and a modicum of curses, I hooked up the laptop and it all worked fine on that - except that I'd "transferred" most stuff to the desktop. It helpfully offered to wipe all my stuff on the iPhone for me, which offer I declined.
Conclusion: something wrong with the iTunes on the desktop (a later version than on the laptop).
Solution: "Repair" the iTunes on the desktop. No need to uninstall and reinstall, which I've done once and will not do again if I can help it - it lost all the music settings and took me ages to sort out the iPod.
Result: All is well. The iPhone is now at 4.1 - I've lost MyWi unless I jailbreak it, but since I have a Voda dongle and don't use the laptop that much now, I can live with that.
Phew!