Ask one of the intended recipients of your missing emails to view their emails via BT's web-based service (rather than by using an email client, such as Outlook, Outlook Express, Windows Live Mail or Thunderbird). If they need the link to the log-in page, it's this:
https://login.yahoo.com/
Ask them to look for a folder labelled 'Spam', 'Bulk', 'Junk' or something similar. I'd be prepared to bet that they'll find your missing mail in there, because BT's mail server is regarding your domain name as a possible source of spam.
Each individual recipient can mark such mail as 'not junk' (or something similar) so that they'll be able to receive your mail in future. Perhaps, if enough people do it, your domain name might get dropped from BT's list of suspected spammers? If not, someone will have to contact BT (which, regrettably, is a task which seems to defeat almost everyone!).
Chris