Seriously though, the "official story" involves 19th lower-class criminals in London coming up with street slang based on their Latin classes...
Don't be daft. The earliest confirmed use according to the Oxford Dictionary is in 1704, so 96 years prior to the C19th; And English has a shit-ton of words derived from Latin, not because some modern (or recent) oik took Latin classes at school, but because the Romans lived in England for a few centuries, and in France for even longer - Latin roots came across the channel with Caesar, and then again with William the Bastard a millennium later (and indeed the OED gives the latter as the path in this case, from Latin to English via Old French)
"Cop" has been a verb meaning "take", "seize" or "capture" for longer than there have been records of English street slang, and a "copper" is, fairly obviously, "one who cops".