If they saw someone external starting up such a scheme they would take it in house as quickly as possible.
If you are running such a scheme you would have complete power over the commercial pilot production in the UK. The airlines would hate it and so would the CAA not having a hand in it.
Also as well that would be a serious amount of cash to be in charge of. It would have a through put of say 40k*1500 a year which would be minimum 60million and very well be over 80million. With a VAT content of over 12million.
And that is just the commercial pilot students not including the PPL's and engineers etc.
Which is why the schools need to continue running their pyramid training schemes getting the money upfriont. If they don't have it they will have to get money at the market rate and will fold.
You would also have something that nobody wants you to have be it airlines, CAA or schools.
You would have the true statistics about the flight training in the UK. How many people start, how far they get how much it costs. The CAA have for years been stopping that info coming out.