With issues and costs surrounding slots at heathrow amongst other problems and disagreements between BAA and BA etc, why don't BA build their own airport?

They have their own terminal, but it is owned by BAA (I assume they owned the land and the runway so they have Heathrow sown up), but surely if they really really wanted they could build their own airport and all of Oneworld could use it. They could then make money, not only on the flights, but also the airport itself along with parking etc.

I can only assume it is something to do with law why they cannot? Unfair monopoly or something?

On that note, are their any airlines that do own their own major airport?

Just curious.