This very symmetrical play has an odd number of characters: nine. Everybody has somebody: Jack and Gwendolen, Algernon and Cecily, Miss Prism and Chasuble, Lane and Merriman. Who’s left out? Lady Bracknell. She’s the only character without a foil or partner.
Lady Bracknell is Wilde’s symbol of the dominant Victorian ethic. As such, she is the most overbearing and powerful character in the play. There is no question, from any character, that the buck stops with her. Her demand for Jack to find a good family drives the action of the play. If she says no, the answer is no. This is a closed society, and no matter what fun the youngsters have, she’s watching and judging them.
As a symbol of the British upper-crust, she passes down the rules and traditions of society and stands in not-very-silent judgment of how the others obey them. When she enters a room, it’s interrogation time:
Lady Bracknell: [Pencil and note-book in hand.] I feel bound to tell you that you are not down on my list of eligible young men, although I have the same list as the dear Duchess of Bolton has. We work together, in fact. However, I am quite ready to enter your name, should your answers be what a really affectionate mother requires. Do you smoke? (I.178)
Jack says yes, and the questioning continues. It’s all going pretty well until he reveals that he doesn’t know who his parents are, and that he was found in a handbag. This. Will. Not. Do. Lady Bracknell snaps shut her notebook and sweeps out "in majestic indignation" (I.218).
What’s so bad about Jack being found in a handbag and having no idea who his parents are? It means he has no name, no background, no class—he may be a peasant for all anyone knows. And Lady Bracknell insists that Gwendolen shouldn’t marry beneath her. Just like the American dream, the Victorian one goes up, not down. And Lady Bracknell has moved up: "When I married Lord Bracknell I had no fortune of any kind. But I never dreamed for a moment of allowing that to stand in my way" (III.77). There’s no way she’ll allow Jack to undo her progress.