It’s not British Slang lol, it’s rarely used and comes from Black / LGBT+ Ballroom culture.
There are slight differences between the two, although you are mostly correct. ‘To clock’ in AAVE and Black LGBT+ Ballroom culture is ‘to notice something someone is trying to hide’, which came in around the 1980s. For general British slang, this started between 1910s-1930s, and means ‘to notice’ in general, not ‘notice something someone is trying to hide’. It’s commonly used, and I hear it in every day British life.
I don’t know what your culture is or your experiences are, but it is just as British as it is Black and Queer Ballroom Culture.
The word 'Clock' itself has been used before in British slang back in the 1900's absolutely (Even at times to indicate violence "I clocked him"), but the modern day usage of it definitely isn't taken from that specific slang. "To Clock It" "I Clocked It" and other examples like in the IF are directly from the Black / LGBT+ Ballroom {American to be specific} and have become much more popular and mainstream in the past few years through things like Ru Pauls Drag Race and Love Island and definitely isn't related to the slang from the 1900's.
Another example would be "Period" it has always been used as way to say "End of Discussion" especially here in Britain but the way it's used now and the reason it's mainstream is because of Ballroom culture not because it's "British" if that makes sense.
I take your point on ballroom culture, genuinely, and I’m not dismissing it, but I think you’re conflating two things.
The way I use “clock” in the IF is “to notice” in the general sense. Characters clock a grin, clock a reaction, clock the vibe. Nobody’s being read, nobody’s cover is being blown. That’s the British usage, which has been in continuous everyday use since the early 20th century, it never went anywhere. It didn’t need a revival via RuPaul’s Drag Race because it was never gone.
The ballroom/AAVE sense is more specific: to see through something someone is trying to hide. Related, yes. The same? No. And crucially, that’s not what’s happening in the text.
Both things can have history with a word without one erasing the other. I’m not claiming British English invented it or owns it, I’m saying when I write it, I’m writing from my own language and lived experience, which is British, and that’s a valid source regardless of what else the word is doing in other contexts.