Green’s Dictionary of Slang dates its usage from the late 19th century; fair in the sense of justifiable:

[late 19C+] (orig. UK Und.):

  • a justifiable arrest; usu. in the tongue-in-cheek phr. it’s a fair cop guvnor, put the bracelets on...

  • any situation seen as fair and about which there is no complaint.

Wiktionary cites an early usage:

1891, Montagu Stephen Williams, Later Leaves: Being the Further Reminiscences of Montagu Williams, Q. C., Macmillan and Co.:

  • "Several other witnesses gave corroborative evidence, and a constable who helped to arrest the prisoners stated that one of them, on being taken into custody, said: 'Ah, well, this is a fair cop.'"

Little Oxford Dictionary of Word Origins notes that:

The verb cop meaning to catch comes from northern English dialect cap meaning to capture or arrest. This probably goes back to Latin capere to take or seize. So a copper was a catcher which is why it became an informal term for a police officer in the 1840s.

Apprehended villains have been saying It’s a fair cop! since the 1880s


According to the Oxford English Dictionary, "cop" in this sense means capture.

My own search of newspapers found a really early example in multiple London newspapers, the earliest version of the story being published on September 1, 1875. A guy was caught breaking and entering and (after a chase) he was brought to the station where he said:

Well, you have made a fair cop (capture) and I'll act square.

(Here's a screenshot of the article, specifically from The Sunday Times on Sunday, September 5, 1875.)

Another early example is in the Derby Mercury (Derby, England), Wednesday, March 27, 1878, which describes a guy who put two fouls in his pockets and got caught. The article says he called it a "fair cop" (here's a screenshot of the article).

The OED also lists an early example for "good cop":

What do you want to search me for? You have got a good cop.
Sessions Paper, 1884

Here's another early example for "fair cop":

Prisoner remarked it was ‘a fair cop’.
The Standard, 1889

The noun came from the verb:

If the Cruel Stork should come, He'd Tyrannize and Cop up some [Frogs].
The Dissenting Hypocrite, 1704

As for where the verb cop came from, the OED thinks it's "[p]erhaps a broad pronunciation of cap" (a now-obsolete verb meaning "arrest" that itself is "apparently [from] Old French cape-r [meaning] to seize").


One early instance of the expression appears in "The Easy Chair," in the [Echuca, Victoria & Moama, New South Wales] Riverine Herald (June 11, 1890):

"It is a fair cop," admitted Mr John Rose, when discovered in company with a jemmy in a house to which he had not been invited ; "but I did not mean to get into the house ; I meant the pawnshop next door." There is an engaging frankness about the explanation.

The British Newspaper Archive turns up an even earlier match—from "Alleged Breach of the Licensing Act at Darlington," in the Daily Gazette for Middlesbrough [Yorkshire] (October 4, 1881) [combined snippets; the paragraph breaks shown are conjectural and almost certainly inaccurate]:

Inspector Scott narrated the facts of the case; and evidence was given by P.C. Ferguson to the effect that on the morning of the day named, about ten minutes to ten, he saw some men loitering about the house. Suspecting something wrong, witness entered the house, and found a man with a pot of beer before him. Mrs Peacock came to the bar whilst witness was there, and when she saw him struck the pot of beer off the counter. The man remarked that there was no use telling a lie about it ; and when witness remarked that it was a fair cop Mrs Peacock appeared very much flurried.

The defence was a total denial that the liquor in the pot was beer. Mrs Peacock deposed that the man who was alleged to have been drinking beer went in her husband's house and asked her for a pint of beer. Mrs Peacock said, Not likely, and the man then asked her for a drink of water, which she gave him. In answer to Inspector Scott, witness denied that the man gave her any money. It was true that Ferguson said to her, This is a fair cop, and she replied, I don't see how you can call it a fair cop giving a man a drink of water. The defendant also swore that the pot contained nothing but water, and his statement was corroborated by another witness, who saw the water drawn.

Eventually, however, the Bench ordered an adjournment of the case, in order to secure the attendance of a witness whose evidence the police and the defence were anxious to obtain.

In each instance, the phrase "It's a fair cop" seems to mean "It is a clear case of catching [someone] in the act of doing something illegal."


From:

The Concise New Partridge Dictionary of Slang and Unconventional English

it’s a fair cop used of a good or legal arrest; in later use, as a jocular admission of anything trivial UK, 1891

and

an arrest UK, 1844 Especially familiar in the phrase IT’S A FAIR COP

Above are a couple of citations showing early use of the phrase, without 'guv'nor.