I've also been hit by not being able to get onto BT Mail since Saturday but this afternoon I got a message from BT that I could in the meantime go back to using my Yahoo account.
So, back on email and there is a message from BT in my Inbox which ends with:
"If you have not been able to find recent emails in your inbox or folders, you can let us know here and we will contact you:" (and a contact email address is provided)
I have lost emails since 6th July, presumably when I migrated. Has anyone else received this email from BT and also lost emails? If so, how long does it take for them to get in touch and re-instate lost messages?