iMac won't let me login with network account
Interestingly, I found a solution for my issue after some testing. In the hope that it helps someone else, this is what I found.

My initial, and many subsequent logins on the device were just Username &amp; Password, and this just stopped working. When I tried domain\username and password it sailed through, asked me to update my keychain, and I was logged in.

That's quite an unusual change of behaviour, as if the device had forgotten that my account was a network account, and was trying to authenticate it locally. There's only one local account configured on the device and the name of it is nowhere close to the name of my network account.

I think I'm going to recommend all users to login using their domain\username as their login name, in order to avoid any support calls for this issue.