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I'm very sorry to hear that you're having some problems with some missing emails. I'm afraid that if they're missing in your webmail inbox and you're unable to find them in either your trash folder or junk/spam folder then they will have been deleted permanently.
Do you have the affected email account set up as POP3 on any other devices via an email client? This would've downloaded the emails from the server onto the device.
I have logged a call with Virgin Media who have raised a ticket to look into whether they can be restored from any backups.
I thought that I had some set up as POP3, but all devices and OS/email clients are showing exactly the same issue - all emails gone, none in any deleted items/trash etc, which leads me to believe this is an issue on Virgin Media's infrastructure.
If it only affects the inbox, that that’s quite a strong hint as to at some point a POP3 connection has been set up (maybe inadvertently), POP3 will pull down the contents of the inbox and marked them as all ‘dealt with and can be deleted’ (not entirely accurate but close enough). If that has happened, them I’m afraid they need to be considered as gone for good, unless you can find the device where POP3 was set up and as long as the account hasn’t been deleted on it, then the missing inbox emails should be there.
FYi, POP3 has no concept of subfolders and doesn’t do anything with Send Items etc - which, if you say are all intact, then really points to a misconfigured client device somewhere. Once POP3 has ‘downloaded’ the inbox and marked all the mail items, then IMAP will assume they have all been deleted and so delete them on all other devices as well.