How has BT kept passwords secure during the migration from BT-Yahoo accounts to BT's own email service?
If the Yahoo system stored passwords "in clear" then that would have been easy, but storing passwords like that is itself an insecure practice. The more secure method would have been to store scrambled version of the passwords (salted and hashed), but migrating passwords stored like that really only works if the target system uses identical salting and hashing.
So which is it? Should we have been warned that it is a good idea to change our email passwords for accounts that have been migrated in case they were handled with reduced security during the migration? The security of email passwords is particularly important because once someone has your email password they stand a good chance of being able to take over your various other accounts using a forgotten password process.