Post-World War I British society was very conservative and hierarchical (that means that social class was super important). Throughout Mrs Dalloway, we see how deeply aware characters are of their social standing. Those in the upper class cherish their family history and often come from royalty or aristocracy; for those in the lower class, it is very difficult to move up in the world. As Woolf clearly indicates, British people were meant to admire the upper class and be very aware of their place in the social ladder. Notice that most of Clarissa’s friends are of the same social status or higher –the prime minister even comes to her party! On the other hand, people like Ellie Henderson and Miss Kilman are loathsome to Clarissa in part because they’re beneath her socially. And it’s not just Clarissa: almost all of the characters are concerned with social status and class – either increasing it, holding onto it, or feeling inferior from it.
Miss Kilman is angry that she’s poor and struggling. Secretly, she may even want to be rich.
Woolf’s attitude toward snobs is pretty ambivalent: she mocks them but also identifies with them.