The fix is to change the Outlook type from "Corporate or Workgroup" to "Internet Mail Only". This stops Outlook being able to connect to an Exchange Server, but has no effect on its ability to connect to a POP3 mail server.

"To do this go to Tools / Options / Mail Delivery / Reconfigure Mail Support and choose "Internet Only". All you need to do then is restart Outlook. An email with multiple recipients where one is rejected will now produce an error showing you the email address which has failed - as opposed to producing the "transport provider" error for every recipient.