Although significantly more than a local taxi - but significantly less stressful I find hotels are much better than BA for transfers. The main advantage is they will know exactly where they are going as opposed to an airline booked one who will be going to lots of different places and may get confused.

If you are flying First then get on the blower to Quintessentially - I forgot to book one via my hotel on a recent trip and the ever friendly guy sorted it all out. I should also add he got 3 quotes for different style of car so it was not a rip off.