Elite was the game that took over my childhood and I remember the great satisfaction I had when I finally made it to 'Elite' status.
I never even thought to look to see if there was an iOS port. I've got a BBC Model B emulator for my HTC One and have the game on that and I still even have a real BBC Model B computer sitting in my parents attic with a copy of the game too.
Thanks OP for asking the question, and huge thanks to JustMe'D for finding the game.