When you leave BT Broadband your email account will be downgraded to a free BTMail Basic account which can only be used on a web browser and not with email clients or email apps such as you may use on mobile devices.
If you want you can "upgrade" back to what you had prior to leaving BT Broadband by paying £7.50 per month to have a BT Premium email account which will return your email account to be the same as it was before you left BT and this can be used with email clients and email apps.
In both instances your email address stays the same.
See link.
https://www.bt.com/help/email/bt-email-products
