someone will correct me if I'm misunderstanding this,
but I'm puzzled why sending mail via BT's SMTP server is an issue, as I assume you are still connected via a BT connection.
My own domain host actually recommends using NTL SMTP servers for sending mail - but this only works while connected via NTL.
I notice the blurb from UKReg mentions 'email forwarding' for the domain registration, but only mentions 'using email' for the extra hosting option - I'm wondering if the domain has to be hosted for email to work properly. If that is the case, there are cheaper options than £3.99 per month.