Here's some advice I sent to a fellow Virgin user - not sure he's had time to try, but it sort of gave me a solution of email that was sitting on the email server, but not downloading to my Apple Mail App.
It seems the Virgin (Blueyonder, Virgin, NTL) issues are being caused through their adoption of Google Mail as their email engine at Virgin. Which means email settings & configs have changed, or need changing... but we are only finding out as it goes wrong!!!
I think I've may have just resolved it - but it's downloaded 1091 emails!... but majority seem to be duplicates of ones already sent.
I went into my Virgin/Blueyonder account and logged into web mail, then chose 'Settings' (top right) and then clicked on, 'Forwarding and POP/IMAP'. The IMAP option was already checked (IMAP enabled) but the POP download had nothing checked... so I checked one to download all mail - mistake as that's what download over 1000 duplicate emails!, and then clicked 'Save changes'.
But the strange thing is whether you check that or maybe the more appropriate radio button named, 'Enable POP for mail that arrives from now on'... none of those radio buttons appear selected if you log-out and log back in again to check??? But the IMAP one does.
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Post note to this is I read somewhere that POP is set as a default, so maybe it doesn't need to be checked, still seems a bit strange though.
Also read that Google password expectation is that your email password is of a minimum strength - many people of course set their password at Virgin, so have a less robust choice. Might be worth changing your password to something Google likes??
Good luck.