I think it is worth remembering how much a place like Heathrow airport is actually worth!! An airport in as premium a place as London (especially for an airport relatively close to the centre) is worth a bomb and I simply don't think BA would even have anywhere near the money to own the terminal or for that matter a significant share in the airport as a whole.

The only exceptions I can think of in terms of airport ownership are airlines which effectively belong to some emir or effectively some extremely wealthy government of the Persian Gulf area.

As others have said, I also don't really see what BA would gain out of it. BA is not in the business of managing real estate and/or airports so even if, for the sake of argument, you thought of T5 owned by BA, they would still sub-contract companies to carry out all the airport related business anyway!