djfingerscrossed,
You're correct in your assessment of traditional contracting in other industries, but you miss the absolutely fundamental and key point that Could/would/should be attacked, which is that to contract AND BE CLASSED AS A CONTRACTOR BY HMRC you must offer your services - and be able to demonstrate that you are doing so - to more than one company.
If you only ever fly for one airline, then it doesn't matter a hoot - you ARE a deemed employee and your salary should be paid under normal PAYE terms, with the employER facing their costs.
IT contractors (an industry I am VERY closely alligned with currently) face this problem continually.
As stated before, BALPA should be arguing the legal point that anyone on flexicrew is actually a deemed employee, which in turn forces the employer to fund NI and tax contributions. The employER in this case might not be easy directly, but PARC, CTC - but the point remains that they can not operate deemed employees without charging.