It is free to have your email accounts moved to a different BT Broadband account
You should be able to do it your self but you may have to contact BT because your new BT account won't have the option to have an email account and this needs to be activated by BT.
https://www.bt.com/help/email/fix-a-problem/problems-with-email/can-i-move-my-bt-email-address-to-an...
