IR 35 regards how you pay yourself and how you are employed by your own Ltd company, ie, payment of dividents and not paying personal tax.
In order to legitimately claim as a contractor you need to have more then one stream of income, therefore working only for BRK would class you as employed by them as they are your sole income. If you were to do other work say through another few agencies then this would help your cause should HMRC take a peek at your books. The only thing is when you register as a company, you have to choose a field of work, so make sure your chosen field is broad enough to cover any other incomes you might have.
With regards to training costs. You can only claim once you are a profession, and therefore only from CPL onwards. This would mean you have to have been able to work for money at that point. The implications would be that your licecnce would have had to be made into a CPL before continuing. This means that intergrated people almost certainly could not claim.
Saying that a CPL pilot could not be employed as a contractor is simply not true as I know a lot of people that have come out of training and got jobs under contract status doing delivey flights and flight instructing. Once you have that CPL, you are a qualified commercial pilot, and any subsequent training you undertake only adds to the likelyhood of more work for your company.