Problem is now resolved by deleting history & cookies, but no, I have never changed my password.
I wish I'd taken some notes or screenshots as I think it was behaving oddly in other ways too, like telling me 'too many login attempts, you'll have to wait a while', or words to that effect, at my very first attempt.
Thinking on that... Maybe I should contrive a number of failed logins so as to deliberately trigger that 'too many attempts' situation. Could it be that the timeout/recovery mechanism was not working, so that once in that state it stays in that state?
I'll try that this afternoon, when I have a moment with the Mac - using the iPad right now.