The link to the archived thread on British Midland in the first post no longer works. There's some applicable information in this current one, though:

Do BMI status match?

BTW, the airline has identified itself publicly as "bmi," not "British Midland," since 2003 - though it's still legally British Midland Airways, owned by holding company British Midland plc.

(Pardon me if this has already been mentioned, but a thread search didn't turn up any occurrences of "midland" outside the first post or others quoting it, and "bmi" is too short to be a valid search string.)