The phrase the butcher, the baker, and the candlestick maker denotes people of various trades or businesses, considered collectively; it has also come to denote anyone at all.

This phrase alludes to the following nursery rhyme, first published in Second Volume of Christmas Box Containing the Following Bagatelles for Juvenile Amusement: High ding a ding, Christmas comes but once a Y^r, Little Tom Tucker, Little Robin Red-breast, Rub a dub dub¹, I’ll sing a Song of Sixpence, Little Boy Blue, Gooseberrys [sic] Grow on an Angry Tree, When I was a Little Boy, Robin a Bobin [sic] a Bilberry Hen, There was an Old Woman living, There were Two Blackbirds. Set to Music by Mr. Hook² (London, 1798):

Dub a dub dub¹.

Duo
Voce 1
Dub a dub dub, dub a dub dub, three Maids in a Tub, three Maids in a Tub, and who do you think was there, there, the Butcher, the Baker, the Candlestick Maker, the Butcher the Baker the Candlestick Maker, and all all all all all of them gone to the fair. The Butcher, the Baker, the Candlestick Maker, the Butcher the Baker the Candlestick Maker, and all of them gone to the Fair.

¹ The nursery rhyme is titled Rub a dub dub on the front page, whereas Dub a dub dub is used as the title and in the lyrics inside the booklet.
² James Hook (1746-1827), English composer and organist

The earliest allusion that I have found to the butcher, the baker, the candlestick maker is from Wanted—a Widow, a short story by the English poet, novelist and dramatist Charles Whitehead (1804-62), published in Bentley’s Miscellany (London) of March 1841:

How to get a housekeeper? Gipps had no more notion of the process by which so desirable an acquisition was to be procured, than he had of the method of calculating by fluxions. He resolved to seek advice upon this head; and who is so capable of giving, and happy to extend his advice, as his old friend Mr. Jackson, a gentleman who had seen a vast deal of the world, and under whose ken housekeepers, without doubt, must frequently have come? He sought Mr. Jackson out accordingly, and made known his wants and wishes—his doubts and his difficulties,
“Very well,” said Mr. Jackson, a gentleman, by the by, whose narrow width of wisdom was eked out by a vast selvage of important gravity, “you want a housekeeper. Well, sir, you want a respectable woman—a highly respectable woman—what I should call a comfortable body.”
“A comfortable body, certainly,” said Gipps; “a comfortable body.”
“Very good, sir,” cried Jackson. “Well, sir, and have you made application to your butcher?”
“My butcher!” exclaimed Gipps. “What in the name of Newgate Market,” thought he, “can ‘my butcher,’ who cuts up beeves and sells them in detail, have to do with housekeepers in their integrity?”
“Your butcher,” resumed Mr. Jackson; “have you, I repeat, applied to your butcher,—to your baker—pshaw! absurd! I was about to say to your candlestick-maker? Let me correct myself. Have you applied to your butcher, to your baker, to your grocer, to your green-grocer? What!” surveying Gipps with surprise, “are you not aware that gentlemen, when they want servants, refer themselves to these purveyors, as, in like manner, when servants want places, they also refer to them?”

The earliest occurrence of the phrase that I have found is from The Morning Post (London) of Tuesday 2^nd May 1848, which published a report from its correspondent in Paris during the French Revolution and the creation of the French Second Republic:

The Assemblée Nationale will be the most variegated meeting that ever assembled. Bos fur sus atque sacerdos³ will be huddled together—priests, peasants, and princes; butchers, bakers, and candlestick makers; unbelieving Jews, credulous Christians, and infidels innumerable.

³ This is from bifrons: custos, bos, fur, sus, atque sacerdos, meaning double-faced: a keeper, a bull (or a cow), a thief, a pig, and a priest (or a priestess), which is a list—that schoolboys would have learned by rote—of second-declension Latin nouns which can be both masculine and feminine.

The second-earliest instance of the phrase that I have found is from The Morning Chronicle (London) of Friday 4^th January 1850, which quoted the review, published in Britannia of 1^st December 1849, of the Post-Office London Directory for 1850:

Let any one […] ask himself what must be the amount of labour required […] to collect together every member of every craft in this huge hive of industry, and to exhibit them, scattered as they are and unknown to each other, in a compact form together, so that any one tradesman, be he butcher, baker, or candlestick-maker, may be picked out, without an instant’s loss of time, from the crowd of his fellows.

An early use of the phrase in the generic sense of anyone at all is from the following, about the abolition of the system of buying commissions in the British army, from Spirit of the Press, published in the Shipping and Mercantile Gazette (London) of Tuesday 21^st February 1871:

The abolition of purchase, observes the Daily News, being acknowledged by the highest authorities as the sine quâ non of the increased security which an organisation, at once elastic and compact, of all the united military forces will effect, it will be curious to hear how those who insist on such an organisation will defend a system which renders it impossible. They will probably contend, as the opponents of free competition for the Civil Services have contended, that the abolition of purchase will “lower the tone” of the service by introducing a new and inferior class of officers; and that every mess and ball-room throughout the British Empire will suffer for the change when the fine young fellows who served their country for less than nothing, and who looked upon soldiering as a manly sport and a gentlemanly pastime, have made way for bookworms and milksops, who will live on their pay, and scarcely own a suit of plain clothes. Where, it will be asked, will be the young heroes of the playing-fields, the foxhunters who followed Wellington, and the curled darlings who stormed the heights of the Alma, when every butcher, baker, and candlestick-maker can send his son into the service?