There's been a number of posts on here asking about the future of BTConnect email addresses. Just to confirm - there's currently no plans to remove BTConnect email addresses, the only change is that basic authentication has been replaced by modern authentication so you will need to log in via webmail to access your emails now. You can find out more here in our FAQs.
You can access your mailbox:
The username and password used to access your btconnect.com mailbox are the same as you use to login in to My Account.
Find out how to recover your login details.