The outbound mail (send) will always be connected to whoever you use as a INTERNET service provider (ISP).
I am unclear from your post, whether you mean BT is the Internet service provider, or simply the provider of broadband to your home.
To try and clarify further, BT provides broadband to me, but I use Pipex as an ISP.
I also have multiple e-mail addresses for various reasons. Each e-mail address is configured to send the mail via Pipex, (because that's who I am always connected to, but each individual (received) e-mail, is configured via it's respective server. I hope that makes sense!