In the unlikely event phone support are unable to help…
What error message do you see when signing into webmail with your blueyonder.co.uk address?

You mentioned that you sign in with your virginmedia.com account and then receive and send using your blueyonder.co.uk email address which indicates it was setup via add email account option, as highlighted below.

In that case emails sent via the blueyonder.co.uk account would appear under its folder hierarchy in the Sent folder as highlighted below:

FYI location of special folders, like Sent, can be determined by:
- select ☰ > Settings > Accounts
- select Edit option for blueyonder.co.uk account
- scroll down to Standard folders section
- confirm Sent messages folder is correctly set (default is Sent folder