The Nazi irony
This novel was published a couple of decades after the horrors of WWII and the Holocaust, events the reader should already know plenty about, but in the story, because Pompey is writing to us from 1936, the Nazi party is kind of a stylish, interesting movement. When she goes to check things out, and she decides that the Nazi party is dangerous and disgusting, the reader experiences dramatic irony, because Pompey doesn't know the full extent of her correctness.
Her friend "Karl"
A Londoner visiting her friend "Karl" who lives in Germany, just before the outbreak of World War II—it's not accidental. Perhaps this signifies that Pompey was open to considering serious social and political reform, and Marx's opinions should be considered, so this scene is a little like her exploring Marxism. That makes her friend Karl's name ironic, because it happens to coincide with the grander interests of Pompey's curiosities about Nazi-ism and Socialism.
Commitment versus control
When Pompey reflects on her engagement, she wonders about all the various ways her boyfriend might have accidentally controlled or influenced her behavior. She was afraid to disappoint him, first of all, and after all, it's not uncommon to get flustered and say the wrong thing, but in her stream of conscious, we see something else going on. Pompey brings attention to all the invisible, uncontested ways that men are allowed to obligate women in her life. Her freedom comes from her unwillingness to be controlled. In any case, her acceptance of an unwanted proposal is ironic.
Gender
Pompey is a powerful person, and she has powerful women as role models in her life, which she teaches us by telling stories about her awesome aunt. The irony is that although in Pompey's opinion, women are often thought to be inferior by others (especially men), she actually becomes more free and autonomous by having to work through the injustices in her society. These types of ironies are common in the novel because she often talks for a long time about her opinion, and Pompey is an ironic, satirical (even sarcastic) narrator.
The irony of religion
Although a free-thinking, powerful woman might have some contention with church, Pompey takes a middle stance, both condemning aspects of religion and the influence of the Catholic church in England, but also heralding people's rights to believe what they want. This comes full circle when she tells her thoughts about the mistreatment of Jews by Nazis (with limited knowledge, because she lives in in 1936). Pompey holds the ironic view that although human religion is seriously flawed, it's part of our freedom to practice whatever religion suits us. Ironically for her, that means none of them.
