I'm afraid to say that this is the first stage (probably) of BA selling BAEC. If you don't think its possible, then I recommend you look at Aeroplan, which Air Canada floated on the stock market a few years ago and which now also owns Nectar.

The logistics are not difficult. As an independent business, The Mileage Company would buy seats very cheaply from BA and would also be paid by BA for miles flown by BA travellers.

The results are very nasty. Aeroplan, for example, only has 2 J seats on each Air Canada flight if I remember correctly. That's it up front.