I've got it now. Apparently /usr has needed to be available at boot
time for a long time, but this seems to have completely passed me by,
and hasn't yet bitten me. I have always thought that 'usr' was short for
'user', and that /usr contains only applications and not system
software. We learn something every day: whether we want to or not.
I can see that I'm not going to be upgrading my server next time, but
rebuilding from scratch, as it has a /usr partition and isn't on LVM.
At the very least, it's a partition rebuild onto another drive. Oh, joy.