After coming across the following questions, Origin of “All right, what's all this, then?!” and Origin of “Well, well, well. What do we have here?”, my curiosity was piqued to try and discover the origins of "it's a fair cop".
According to the Urban Dictionary, it's
a phrase roughly meaning "Eh, I guess it's fair."
The Longman Dictionary of Contemporary English defines "it's a fair cop" as
British English spoken used humorously when someone has discovered that you have done something wrong and you want to admit it
British English used humorously to admit that you should not be doing something that someone has caught you doing
• It's a fair cop - honest, officer!
• And criminals are warned that from then, they won't even have time to tell police it's a fair cop.
• Do you want me to say that it's a fair cop or something?
TV Tropes says
In any given Crime and Punishment Series or film, the chances of encountering a Fair Cop are high.
A Fair Cop is any police officer who is ridiculously attractive, ridiculously young, or both. This should not, however, carry with it assumptions that they are dumb. Call it the police version of Hot Scientist or, even closer, Good-Looking Privates. TV cops almost never have a mustache.
The title is a play on the British and Australian expression "It's a fair cop", said when one admits having been caught fair and square. See also Firemen Are Hot and Good-Looking Privates. Cousin to Hot Men At Work.
You are not particularly likely to see a Fair Cop in a stripper's police outfit — although you may see him or her as a Dirty Harriet, which gives a whole new meaning to the motto "To protect and to serve".
If you're looking for a fair-minded cop, you're probably looking for Reasonable Authority Figure or maybe a By-the-Book Cop (who usually fits).
From a Q&A on worldwide words discussing the phrase.
Q: ... In one of the Monty Python movies, as a woman falsely accused of being a witch is being carted off to her destiny she says under her breath, that’s a fair cop! ...
A: It’s a well-understood British expression, though it has been used so often in second-rate detective stories and police television series down the decades that it has long since ceased to be possible to use it seriously (the Monty Python team was playing on its clichéd status).
It comes from the same root as the term cop for a policeman. This may be from the slang verb cop, meaning to seize, originally a dialect term of northern England that by the beginning of the nineteenth century was known throughout the country. This can be followed back through French caper to Latin capere, to seize or take, from which we also get our capture. (See also the piece on cop, a policeman.) So a cop in this sense was an example of a seizure or capture.
It’s a fair cop was what the essentially good-natured thief with a typically British sense of fair play was supposed to say as his collar was fingered by the fuzz, meaning that the arrest was reasonable and that he really had done what he was accused of doing. You will understand that this is, and always has been, an entirely fictitious view of the relationship between British criminals and the police.
This answers the "cop" part, but doesn't delve into the "fair" component of the expression and the concurrent use of the words.
I understand the meanings of "fair" and "cop"! I'd like to know when and how the words came to be paired together.
Researching "fair cop" in the Online Etymology Dictionary didn't get me very far.
They provide the following
Old English fægere "beautifully," from fæger "beautiful" (see fair (adj.)). From c. 1300 as "honorably;" mid-14c. as "correctly; direct;" from 1510s as "clearly." Fair and square is from c. 1600. Fair-to-middling is from 1829, of livestock markets.
"policeman," 1859, abbreviation (said to be originally thieves' slang) of earlier copper (n.2), which is attested from 1846, agent noun from cop (v.) "to capture or arrest as a prisoner." Cop-shop "police station" is attested from 1941. The children's game of cops and robbers is attested from 1900.
A user on Word Reference answering a question about a French equivalent for "It's a fair cop, guv'nor." suggests
The phrase goes back to the 19th century. Popularized by the novel Raffles, 1899.
Can anyone corroborate and expand on this?