Your eMail address will downgrade to a PAYG - Pay as you go address. You won't actually pay anything, it is a reference to the old dial up days. You will be able to recieve eMails to this address but you will need to use the outgoing mail server from your new Internet service provider.
The messages will still appear to come from you / your company, and the reply will go to email@example.com and as long as you keep using it it will be active.
Be sure to tell BT that you want to keep the eMail address when you close the account.