Are Brits unusually sensitive to aspersions on their class origins?

I agree with your overall point, but you’d most likely be dead wrong about me. I came from the bottom end of society; public housing, family surviving on my dad’s disability pension (disabled war veteran) - but I lost my poor kid accent without even trying, my family was dirt-poor but we were a family of readers who went to the library religiously, and I was always interested in things like fine art. I’ve always liked writing and put a fair bit of effort into spelling and grammar. So people assume I went to a nice school and lived in a nice house.

Now, I’m not the least bit interested in fooling anyone or pretending to be anyone I’m not, but you don’t have to look too hard to find stories of impostors tricking people into believing they’re from the upper classes. The assumption that people from poor backgrounds always talk, dress, and act like poor people is very foolish indeed. Some of us you’d never know unless we told you.

ETA: Yes I know you said “often” - I’m just saying “more often than you’d think”.

That’s one example of what people mean by being poor financially but middle class culturally. Others would be the ‘starving artist’ type, or the grad student type.

Books and art are some of the most obvious class signifiers in the US. This may fade in time as more people choose ebooks, but I will probably never get rid of all my books even if I never read them. I know that if I am in a person’s house for the first time I notice whether they have any books.

Vocabulary and speech patterns are also a sign of someone’s social class. Accent, with some exceptions, generally isn’t. It’s not always obvious though, because middle class Americans are so used to code switching that we do it without realizing that we’re doing it.

Food choices also vary, the most obvious one being a preference for wine or mixed drinks vs. beer.

I suspect that was made up and never actually happened (your co-worker’s story, not yours). It sounds like stealth-bragging about his working class credentials.