Digitalis I meant that BA would buy one of the companies and scupper the deal. I know BA are very keen to reduce their debt but this would be a very rare event where they could gain more control at heathrow and I think the banks would see the logic in the deal.
I think there would be a very good chance of the competiton authorities allowing this to get through as the EU let the AF + KL merger through and the UK might as well because of all the LCC competition.
As for both being private companies, they still have owners and if BA offered a good deal to say Bishop then BA could still pull it off.