Oops. Confession time. I mistyped the password previously when I received the authentication failed message.
But now, when I input the a1 login message (following '* OK Virgin Media IMAP4 server ready [ e4c558782VM ].'), it just comes back with the message 'closed' whether I get the password right or wrong. I've even tried rebooting but that doesn't make any difference. I feel I must be doing something silly, but I don't know what it is.
Well, I'm feeling rather shame-faced now. The problem was the most obvious error of all! It hadn't occurred to me that the password I use to log in to the website is the same as the password I use to download my emails. I don't know how long ago it was I changed my website log-in password, so long ago I can't remember doing it, but I'm sure I had never changed that password on my Outlook server settings. It was only the Virgin Media outage that made the connection have to start up again and fail the password test.
In fact, when I went to change the password in Outlook via the Server Settings page, it errored when I tried to do it. I looked up the error and was shown a different mechanism to change the password. That's not proof I'd never changed the password in Outlook, I know, but it is an indication.
So, my problem is now resolved! Many thanks to everyone who helped me, particularly Tim, who has patiently moved from diagnostic to diagnostic, but also to Howard and to the guys at Virgin Media. I could never have fixed it without your help.
So pleased you got there. I didn't do that much but I accept the compliment. Kudos to you for the way you have handled tis and finally summarised the issue. That helps us all build a community of answers.
As a Very Insightful Person, I'm here to share my knowledge. I don't work for Virgin Media.