Symbolism, Imagery, Allegory
Welch's "fawn fishing hat" is only mentioned a handful of times in this book, but it's enough of a quirk to serve as one of the dozens of things that annoy Jim about Processor Welch. Imagine an elderly history professor wearing it around campus. It's Amis's symbol of everything that's ridiculous to Jim. It has no point. Welch is a professor of medieval history, not a person likely to spend his weekends hauling flounder out of the lake.
The fishing hat makes its final appearance in the book's last scene, when Jim runs into the Welch family while escorting Christine (his recently acquired GF) to a restaurant. Jim notices that Bertrand's "beret, however, [is] on Welch's head, the fishing-hat on Bertrand's" (25.65). Bertrand's beret is like a companion symbol to Welch's hat, in the sense that both men seem to wear these hats just for the sake of making a statement. Problem is, Jim thinks these statements are fake: "I'm a country lad at heart"; "I'm too too French for you to appreciate."
The fishing hat and beret signal that Bertrand and his father are impostors. Amis confirms this point when he shows the father and son switching hats, which suggests that the hats themselves don't matter as long as each man wears something that makes him feel distinctive.