I rang customer services, who said my inbox was locked (they didn't now why) and they unlocked it themselves by changing to a new password. It wasn't till 4pm that I got an email from Virgin Internet Security telling me they'd locked the inbox because of "suspicious activity". They told me to change my password (so I changed it again) and run a virus scan (which I did - nothing found).
It would have been helpful if Security had told me a few hours earlier what they had done! I had no way of telling what had happened.