First of all (see last post), we're four steps from Alistair Sim.
For years, watching the Alistair Sim version of Scrooge, we've sworn the sweet, silent -- and uncredited -- little maid who lets him in to see his nephew is Audrey Hepburn.
Finally we think we've got a reasonable argument: Audrey Hepburn has a very small speaking role in Laughter in Paradise, a film that includes Alistair Sim, George Cole, Eleanor Summerfield, and possibly two others, who all appear in Scrooge. It's the same actor's pool.
That's certainly Hepburn, and that makes it five steps to Eliza Doolittle.
Another way: Don Taylor, directed by Billy Wilder, who directed Audrey Hepburn. Easier, but not so much fun!