In British English, the noun cricket is colloquially used to denote:
1-: the game of cricket played in the correct manner or proper spirit;
2-: hence, more generally, fair play, i.e., honourable dealings between opponents or rivals in any sphere.

This use of the noun cricket occurs chiefly in negative contexts (especially in the phrase not cricket) to denote something contrary to traditional standards of fairness or rectitude.

The earliest occurrences of this use of the noun cricket are as follows, in chronological order:

1-: The noun cricket in the sense of the game of cricket played in the correct manner or proper spirit:

1.1-: From Volume II of The Confederates: A Story, in three Volumes (London: Printed for T. Hookham, 1823), by Abel Moysey:

This was an adventure undoubtedly; but not of so interesting a nature as to interrupt Ullesbey’s slumbers, or even derange, for above ten minutes, the former current of his ideas; which ran much upon the noble game of cricket, the indifferent innings that had fallen to his own share in the course of the day, and the superior success to which he might reasonably look forward on the morrow, now that (as he flattered himself) he began to comprehend their method of bowling. It was all a trick, he settled, just as he dropped asleep—not the real, old, legitimate system of play—not cricket, properly so called; but all a deception.

1.2-: From The Cricket Field: Or, The History and the Science of the Game of Cricket (London: Longman, Brown, Green, and Longmans, 1854), by James Pycroft (1813-1895):

A spinning ball is the most mischievous; and when there is spin and pace too (as with a ball from Mr. Fellowes, which you can hear humming like a top) the danger is too great for mere amusement; for when, as in the Players’ Match of 1849, Hillyer plays a bowler a foot away from his stumps, and Pilch cannot face him—which is true when Mr. Fellowes bowls on any but the smoothest ground—why then, we will not say that any thing which that hardest of hitters and thorough cricketer does, is not cricket, but certainly it is anything but play.

2-: The noun cricket in the sense of honourable dealings between opponents or rivals in any sphere:

Context: During the Boer War (1899-1902), in reference to the colour of the uniforms worn by the British troops in South Africa, the noun khaki was used to designate wartime policies, sentiments, etc. In particular, the expression khaki election was used of the general election of 1900, regarded as influenced by war. The nouns khakiite and khakiness designated, respectively, an enthusiast for wartime policies and enthusiasm for wartime policies.

2.1-: From The Westminster Gazette (London, England) of Tuesday 5^th June 1900:

There is one announcement of Ministerial movements which is decidedly interesting:
Mr. Balfour arrived in London on Saturday from Hatfield, and proceeded to Hardwicke Hall, the Derbyshire seat of the Duke of Devonshire, on a visit to the Duke and Duchess.
We may be pretty sure that the General Election will be one of the subjects of discussion. We should be very much surprised if the Duke really thought that to dissolve would be “cricket,” but then (as the National Review has said) the Khakiites are very strong, and the Duke is hardly likely to prevail against his more pushful colleagues. In fine the decision rests with Lord Salisbury. Did he agree with Lord Beaconsfield that a “Peace with Honour” dissolution would have been a constitutional breach? If not, we see no reason why he should not agree with Mr. Chamberlain in rejoicing in Khakiness.

2.2-: From The Westminster Gazette (London, England) of Tuesday 31^st July 1900:

THE “NO OPPOSITION” LEGEND.

[…] The Birmingham Daily Post is a strongly Unionist journal, and has always supported Mr. Chamberlain’s South African policy. But it is dead against an autumn election on an issue solely confined to the war. It would be “contrary to all modern experience” to appeal to the country on “a register that is almost dead” and only “urgent necessity” could justify a course that would “disfranchise many thousand citizens.” Does the “urgent necessity” exist? The answer is said to be No. There is no sufficient practical issue on the settlement after the war; as to its conduct there is “no sufficient evidence available to allow of a fair verdict.” Besides, it is impossible to overlook the Chinese question. “It would be a startling innovation were a Prime Minister, who is also Foreign Minister, to launch the country upon a General Election when on the greatest foreign question of the hour he must confess himself in the dark as to the facts, and consequently undecided as to his policy.”
We hope that these “few plain words” will have the effect of letting the Government know that it is not only Liberals who see the impropriety of a Khaki election. As a fact, we believe that the feeling is very widespread that it would not be “cricket” to get back to power again as the result of an appeal to the country in which every other question and every part of the world was sponged out by South Africa. No one imagines that in the election, whenever it comes, the South Africa question will not play a prominent part, but that is altogether different from so arranging the appeal to the country as to get advantage of the “boiling-point.”

Likewise, the phrase to play cricket is colloquially used, frequently in negative contexts, to mean to act fairly or honourably. The earliest occurrence is from Some After-Dinner Speakers, by Harry Furniss, published in The Strand Magazine: An Illustrated Monthly (London, England) of September 1902:

The best after-dinner speaking I ever heard was at a dinner where half-a-dozen speakers—all English—made far more eloquent and more witty speeches than I have ever heard at half-a-dozen American show banquets. […] All the speakers confined themselves to their subject. Now this the Americans seldom do, as I have just pointed out. They give a string of anecdotes, good, bad, and indifferent, and wind up with an eloquent peroration in flamboyant style. There is decidedly too much playing to the gallery and too little “playing the game,” as we would say, in order to drag in a story. The best friends of the speaker are bowled over without the least compunction. This is not playing cricket, but it is what I have witnessed Chauncey Depew and all American show dinner orators play at. It is what their friends expect and enjoy. We have a higher motive, and we therefore have better speeches.