For me, When I browse to https://mail.blueyonder.co.uk/ with Opera 12.14, there is an immediate redirect to the site below which provides the log-in page:
If you examine that URL, you can see it makes use of services at Google.com. The Google support page (www.support.google.com/accounts/answer/32050) that's displaying on his system has to do with clearing browser cache and cookies, so I'm guessing that something incorrect in either of those locations is interfering with the redirection involving Google. I suggest he clear both cache and cookies and try it all again: ctrl+F12 > Advanced > History > at Disk cache, click on Empty Now > OK; then ctrl+F12 > Advanced > Cookies > Manage Cookies > delete any cookies related to blueyonder, virginmedia, and google > OK.