BA Complaints
A few years ago I had a fairly minor complaint with BA which I registered through the normal channel. I received no response despite resending it twice so eventually I wrote to Michael Street, who at the time was Customer Service Director, copying all the previous correspondence. I had a call almost immediately from a very helpful guy in Customer Service who told me that he had been appointed to make sure that my complaint was dealt with to my satisfaction. We agreed what I felt was a very generous arrangement and the guy told me to contact him again with any further problems.
I suggest you try the regular customer service route first and if you don't get an acceptable response write to the office of Geoff Want, Director of Ground Operations.
Can't help you with Qantas.