I have just checked my Virgin media e-mail account - the one using their web site - and find that all my sent and inbox messages appear to be present. However, my account setting on that site is IMAP, as is the one I have in Thunderbird.
On the other hand, Thunderbird has been problematic and, for that reason, I downloaded Microsoft Office Outlook which I now use as my default e-mail client. Strangely, though, this is listed as POP rather than IMAP. Nevertheless, all messages appear to be in there as well.
I'm sorry that I can't be of more help, but e-mail accounts (along with many other computer-related matters) remain a complete mystery to me!
I do remember, though, that a few years ago I had some e-mail problems and contacted Virgin for help. I wish I hadn't as, at the time, the 'expert' (a woman with a 'foreign accent', so likely an offshore call centre) asked for permission to take control of my computer, which I agreed to. Unfortunately, she advised changing my account details (again which I agreed to, as I trusted Virgin staff to know what they are doing - I don't any more!) and she promptly lost all my messages - received and sent.
Of course, I complained and another expert (Scottish this time) spent several hours talking me through some procedures to restore my inbox messages, but all sent messages were irretrievably lost.
For that reason, I suspect that the Virgin people you spoke to and who said that 'they cannot help' may indeed have been telling the truth.
If I were you, I'd raise a formal complaint with Virgin. I hope you have more success than I did.
