Pompey's friend "Karl"
There's a symbolic adventure in the story when Pompey visits Karl in Germany. Obviously this sounds like a reference to Karl Marx, so the passage might be an allegory indicating Pompey's experimentation with Marxist philosophy, journeying to Germany to see the ideas in practice, and deciding that Marxism is disturbing. Why is it disturbing? Because Pompey can't help but remember how easily hatred turned Marxism into straight up Nazi-ism, not 20 years earlier.
The yellow paper
The idea of someone writing a novel on yellow paper is interesting because it's the only reference to Pompey writing her novel, which means basically, that it's still Stevie Smith talking at that point. Her yellow paper is a clue to the reader that she is not a novelist, that she has another version of writing that is more normal and ordinary (for Smith, poetry; for Pompey, paperwork), but she is deciding to try her hand at a novel. This scene ends with a break in the fourth wall where Smith just says bluntly that her novel isn't supposed to be like any other novel. It's weird, and reader beware.
The false engagement
When Pompey decides not to marry her boyfriend, and then he proposes, she accepts anyway, raising the question: Why did Pompey do what she did not want to do? The answer is that this is a symbol for the unspoken, unseen ways that various social practices disenfranchise women. In other words, she felt obligated to do what he wanted, and perhaps she felt nervous about his fragile ego. Regardless, it nags at her until finally she confronts him.
The Catholic church
When the church gets brought up, the assumption based on Pompey's character is that she won't have high regard for the church, given her critical opinions on other things. But actually, she strikes a balance. Her criticism of the Catholic church should be held in tension with Pompey's advocacy for Jews (this was only a few decades after the Holocaust, remember), meaning that although Pompey believes that the church should not be able to compel people to attend mass or believe anything, she does defend the right to religion.
Nazis
Now, to be sure, because of the timing of this novel's publication, because it was written by a Londoner, there doesn't need to be an explicit reason for this novel to mention Nazis. The interesting part of this symbol is that the Nazis have not been exposed for their true evil yet, and when Pompey goes to Germany to check things out, she notices (before WWII has broken out) that the system is motivated in an evil way. She gets freaked out and leaves.
