Often, the argument for outsourcing is not to save money on the service itself, but to reduce the management overhead (in focus and attention terms) and allow the cocpany to focus on its core business.
Money is a factor but so is flexibility. It's a lot easier to change supplier to one that has a better product/deal.
I'm slightly surprised that BA seems to have put ALL it's business through this one supplier. It's called being "single sourced". Perhaps they should have had two suppliers to reduce the risk.