There are plenty of threads about people having similar problems, with most answers suggesting checking your browser's security settings and/or deleting your cookies, and with VirginMedia suggesting a password reset. e.g. here:
http://community.virg...le-chrome/td-p/984775
and here:
http://community.virg...g-an-Email/td-p/82508
Try using the lowest possible security settings within Chrome. (It won't do any harm for a short while, particularly if you're only trying to access a trusted site).
However, if you're only accessing your mail from a single computer, it would make far more sense to use a dedicated email client, rather than webmail, anyway.
Chris