Has this always been the case or has it just started that it does not work.
Have you checked that you have the correct settings as per this link.
http://bt.custhelp.com/app/answers/detail/a_id/44917/kw/bt%20mail/c/346,6588,6591
There could be 3 diff providers involved in this:
Are they all BT?
But SMTP is just used for sending. I thought your issue was receiving over WiFi?