While the advert may be grating on British sensibilities, as an American, I think it does quite well. There is a limit on how much factual information the typical punter can absorb over a minute, so the goal is to leave him/her with a feeling that s/he will remember every time s/he thinks of the airline. Here, the intended feeling is that BA has been trusted and reliable for the last century -- and isn't that what you are looking for when you choose to fly?
I can see the punchline "to fly, to serve" as being the basis for a huge amount of follow-up advertising over the coming years. It could become as iconic as "Singapore Girl" or United's (Gershwin's, actually) Rhapsody in Blue as being the public's symbol for the airline. I guess we'll see ...