The phrase the oldest profession in the world, and its variants, designate prostitution.

This phrase occurred, for example, in the following, by Joy Lo Dico, published in the London Evening Standard (London, England) of Monday 25^th September 2017 [page 20, column 2]:

Brexit red light for the world’s oldest profession?
FIRST there was Brexit. Now Sexit? The sex workers of London are particularly worried over what will happen when we leave the European Union. The English Collective of Prostitutes note that the majority of those working in London are from abroad, in particular from the former Eastern Europe.
Prostitution is legal in the UK but the problem is, with Brexit, whether the Home Office decides to classify it as a legitimate trade for foreign workers to pursue in this country.

Note: Before the oldest profession in the world came to designate prostitution, this phrase was applied, with positive connotations, to various professions, trades, arts, etc.

It was especially agriculture that the oldest profession in the world designated—as in the following, about the laying of the foundation stone of a farm school at West Buckland, in Devon, published in The Western Morning News (Plymouth, Devon, England) of Monday 15^th October 1860 [Vol. II, No. 245, page 2, column 3]:

Agriculture is every day becoming more of a science. Chemistry and steam have revolutionised the oldest profession in the world.

As an example of the various—and occasionally curious—uses of the phrase, the following paragraph is from The Journal (Logan, Utah, USA) of Saturday 16^th September 1893 [Vol. XII, No. 73, page 7, column 3]:

The healing art, par excellence, is claimed by theological chronology, the most ancient profession on earth since the first man eat [sic] the indigestable [sic] apple, and is backed by all materialistic anthropologists, who assign dates to the profession before the birth of Adam.

The earliest occurrences that I have found of the phrase the oldest profession in the world and variants applied to prostitution are as follows, in chronological order:

1-: From the first paragraph of On the City Wall, in In Black and White (Allahabad: A. H. Wheeler & Co., 1889), by the English poet, short-story writer and novelist Rudyard Kipling (1865-1936) [page 78]:

Lalun is a member of the most ancient profession in the world. Lilith was her very-great-grandmamma, and that was before the days of Eve as every one knows. In the West, people say rude things about Lalun’s profession, and write lectures about it, and distribute the lectures to young persons in order that Morality may be preserved. In the East where the profession is hereditary, descending from mother to daughter, nobody writes lectures or takes any notice, and that is a distinct proof of the inability of the East to manage its own affairs.

2-: From Wanted a Patriot, published in The National Observer: A Record and Review (Edinburgh, Midlothian, Scotland) of Saturday 27^th August 1892 [Vol. VIII, No. 197, page 370, column 1]—the following is about “the thirty thousand Englishmen upon whose fitness and loyalty the British raj is based”:

The private soldier will not deny himself obedience to certain physiological laws, nor were it well for efficiency that he should. The army regulations and the fitness of things do not permit his marriage: Lord Roberts cannot have such a following of wives and nursemaids as crossed the Hellespont with Xerxes. Whence the necessity of ‘the oldest profession in the world.’

3-: From an article about barmaids, published in The Umpire (Manchester, Lancashire, England) of Sunday 22^nd January 1893 [No. 465, page 1, column 6]:

We all know perfectly well that it is not because barmaids are barmaids that they are condemned by certain austere censors. It is because they are credited with being something else. Because, in fact, they are supposed to belong to what Rudyard Kipling assures us is the most ancient profession on earth.

4-: From Round the Town with Dr. Johnson, by George Whale (1849-1925), published in The Gentleman’s Magazine (London, England) of February 1893 [Vol. CCLXXIV, No. 1,946, page 128]—the following is about Ranelagh, a public garden at Chelsea:

It must once have been a merry, yet proper place; for the expression “Ranelagh Girl” became common, and, happily, did not mean one who belonged to what has been called the “oldest profession in the world,” but a “lively young lady of excellent principles.”

5-: From a negative review of The Story of a Dacoity and The Lolapur Week: An Up-Country Sketch (London: W. H. Allen & Co., Ltd., 1893), by G. K. Betham—review published in The National Observer: A Record and Review (Edinburgh, Midlothian, Scotland) of Saturday 20^th May 1893 [Vol. X, No. 235, page 21, column 1]:

Worst of all, he [i.e., G. K. Betham] regrets that the ‘oldest profession in the world’ is ‘truly a pitiable state of things to exist in civilised India in the last quarter of the nineteenth century!’

However, G. K. Betham did not use the expression the oldest profession in the world in The Story of a Dacoity and The Lolapur Week. The review published in The National Observer was referring to the following passage from page 26 of G. K. Betham’s book:

Yelama is the goddess to whom the Bèders are most devoted […]. The third daughter of every Bèder is vowed to this goddess, and is sent to her temple when about ten years of age; they are attached to the temple service for a time, and then drift away into the villages, where they lead the lives of prostitutes. The system is, in fact, no more nor less than prostitution sanctioned by religion. […] Truly a pitiable state of affairs to exist in civilised India in the last quarter of the nineteenth century!

6-: From Massage and Aristocracy, published in Reynolds’s Newspaper (London, England) of Sunday 22^nd July 1894 [No. 2,293, page 4, column 4]:

In ancient Rome, under the Empire, ladies used to go to baths to meet a certain class of men; while men resorted thither to meet a certain class of ladies. The ladies belonged to what has been called “the oldest profession in the world,” a profession which is carried on in Piccadilly, Regent-street, and other parts of modern London with great energy every night; and the men were the male parallels of that particular class.

7-: From London after many Years.—II., by ‘H. H. O.’, published in The Civil & Military Gazette (Lahore, Punjab, Pakistan) of Saturday 29^th July 1893 [Vol. XVI, No. 5,124, page 1, column 4]:

It is now 13 years since I last saw London, and I must say I find it wonderfully improved. […] The first night I arrived in town I went to the Royal in Holborn, a music hall of about the average London quality. In my day it would have been impossible to take a lady to a place of this kind, but I found to my astonishment and gratification that the whole tone of the Variety Entertainment has altered. […] I sat through a long, but quickly varied, programme of 20 events, and there was not one word, nor one action, on the stage which could have offended the most fastidious taste, or which a child might not have listened to and seen. There were of course a number of members of what Rudyard Kipling calls “the oldest profession on earth” present, but they were not much “en evidence,” and no loud behaviour of any kind would be tolerated for one moment by the stalwart “chuckers-out” (most of them old soldiers evidently, and dressed in handsome uniforms, with frock-coats and forage caps, like Staff officers) who guard all the doors and patrol the different parts of the auditorium.

—Cf. also the second-oldest profession (in the world).