The British-English phrase beer and skittles denotes unmixed enjoyment.

The image is of a person drinking beer while playing skittles, as is clear from the following instance of beer and skittle used in collocation; on Thursday 25^th August 1831, The Globe (London) published an article about the remedies that “the friends of morality and good order” want to provide for “the corruption of public morals […] flowing […] from the beer-houses”:

The Bishop of London wishes to prohibit the union of beer and skittle-playing, as the exercise tends to promote thirst, and to make the immoral liquor more agreeable and effective.

The following announcement from Aris’s Birmingham Gazette (Birmingham, Warwickshire) of Monday 14^th August 1837 shows that skittles were a feature of public houses:

THE BARREL PUBLIC HOUSE,
Barr-street, corner of Great King-street.

BY I. ALLEN.—To be SOLD by AUCTION, on the premises, on Tuesday, August 22, at ten o’clock in the morning (in consequence of the extreme indisposition of the proprietor), the valuable Licences, Good-will, and Possession of the above convenient and good accustomed establishment, also the Brewing Utensils, Fixtures, Stock in Trade, and part of the Household Effects, comprising ale, beer, porter, cider, skittles and pins, excellent hogshead and half-hogshead barrels, twenty-strike mash-tub, coolers with lead pipe, furnaces, grates, doors, &c. setting, oval and round tubs, four-pull ale machine, screens and benches, drinking tables, Windsor and other chairs, cups and tankards, glass and earthenware, sign-boards, and other effects, to be particularized in catalogues, to be had on the premises, at the offices of I. Allen, Smithfield, and Allen and Son’s, West Bromwich.

The earliest instance of the phrase that I have found is from the Nottingham Review, and General Advertiser for the Midland Counties (Nottingham, Nottinghamshire) of Friday 26^th August 1831:

House of Commons, Wednesday.
On a petition in favor of the present Beer Act, a very long debate ensued […].
Mr. O’Connell said the charge of cant attached to those, who, under the plea of morality, wish to re-create an odious monopoly of brewing and licensing; the House might as well spare itself the constant interference with the enjoyments of the poor; if they legislated at all, they ought to extend it to the club houses, and regulate the quantity of champagne to be drank, or the amount of play at Crockford’s, as well as to the poor man’s beer and skittles.

During the description of Fleet Prison in The posthumous papers of the Pickwick Club (London, 1837), the English novelist Charles John Huffam Dickens (1812-70) makes Sam Weller use the variant all porter and skittles:

(1851 edition)
“It strikes me, Sam,” said Mr. Pickwick, leaning over the iron-rail at the stair-head, “It strikes me, Sam, that imprisonment for debt is scarcely any punishment at all.”
“Think not, Sir?” inquired Mr. Weller.
“You see how these fellows drink, and smoke, and roar,” replied Mr. Pickwick. “It’s quite impossible that they can mind it much.”
“Ah, that’s just the wery thing, Sir,” rejoined Sam, “they don’t mind it; it’s a reg’lar holiday to them—all porter and skettles. It’s the t’ other vuns as gets done over vith this sort o’ thing: them down-hearted fellers as can’t svig avay at the beer, nor play skettles neither; them as vould pay if they could, and gets low by being boxed up. I’ll tell you wot it is, Sir; them as is always a idlin’ in public houses it don’t damage at all, and them as is alvays a vorkin’ ven they can, it damages too much.

The phrase also appears in early use as a proverb, (this) life is not all beer and skittles; the earliest instance that I have found is from Nature and Human Nature. By the author of Sam Slick, the Clock-maker (London, 1855), by the Nova-Scotian author Thomas Chandler Haliburton (1796-1865):

“Cutler,” sais I, “come back, that’s a good fellow, and I’ll tell you the story. […] There was a jack-tar once to England who had been absent on a whaling voyage for nearly three years, and he had hardly landed when he was ordered off to sea again, before he had time to go home and see his friends. He was a lamentin’ this to a shipmate of his, a serious-minded man, like you.
“Sais he, ‘Bill, it breaketh my heart to have to leave agin arter this fashion. I havn’t seen Polly now goin’ on three years, nor the little un either.’ […]
“‘It seemeth hard, Tom,’ said Bill, tryin’ to comfort him; ‘it seemeth hard; but I’m an older man nor you be, Tom, the matter of several years; […] and my experience, Tom, is, that this life ain’t all beer and skittles.’
“Cutler, there is a great deal of philosophy in that maxim: a preacher couldn’t say as much in a sermon an hour long, as there is in that little story with that little moral reflection at the eend [sic] of it.”
“‘This life ain’t all beer and skittles.’ Many a time since I heard that anecdote—and I heard it in Kew Gardens, of all places in the world—when I am disappointed sadly I say that saw over, and console myself with it. I can’t expect to go thro’ the world, Cutler, as I have done: stormy days, long and dark nights are before me. As I grow old I shant be so full of animal spirits as I have been. In the natur [sic] of things I must have my share of aches, and pains, and disappointment, as well as others; and when they come, nothing will better help me to bear them than that little, simple reflection of the sailor, which appeals so directly to the heart. Sam, this life aint all beer and skittles, that’s a fact.”