I don't have any experience with BMI on this but have fought with BA quite a number of times about this. The right answer is Yes you should be allowed the long haul baggage allowance if you are on one ticket. Now I don't know how well trained the BMI staff is at EDI but at NCL the BA Swissport staff are really bad! People go on about lounge dragons, these people are check-in dragons! They don't want to hear anything.

I have traveled on BA/Jet ticket 4 times in the last year and have been allowed the long haul allowance 3 times with major issues. By this I mean that I have to show them a page from their own training manual that states that if on one ticket then the higher baggage allowance applies. Last month she was so rude that I had to pay 35 pounds per bag and that also till LHR where I had to pick up my luggage and check-in again! She would not even look at her own training manual and claimed that no manager was around!

How ever I feel BMI staff will be better. Yes you are allowed the long haul allowance, its up to you to convince the under trained check in staff.