The story is told by someone who's well outside of the story. Check out the very first line:
Once on a dark winter's day, when the yellow fog hung so thick and heavy in the streets of London that the lamps were lighted and the shop windows blazed… (1.1)
It's told from a detached point of view, and the source knows everything about the characters, from how Miss Minchin feels about Sara to why Lottie is having a tantrum to how hungry Sara and Becky are. That's pretty omniscient.
Although there are characters we never get to see inside of--most notably, Anne, the little beggar girl. Why do you think we never get her feelings or thoughts?