Envelope-licking became a thing in the 1840s in the UK, and then in Europe and in other parts of the world. It was the consequence of a series of changes: the reform of the postal service in the UK and France, the widespread adoption of the envelope, and the development of machines that could mass produce adhesive stamps and envelopes.

People found it icky from the very beginning, and never stopped.

Gummed envelope rising!

Envelopes (from the French enveloppe, it lost a p when crossing the Channel) started being in use in the 17th century in France. Before that, people just folded (or rolled) their letters and closed it with a seal. The first Dictionary of the Académie Française (1694) has an entry for enveloppe but only mentions packages. It also says that "écrire sous l'enveloppe de quelqu'un" means "putting one's letter in someone else's package." The dictionary of Antoine Furetière (1701) says that one could send letters under a "double envelope". In 1726, Jonathan Swift wrote in his poem Advice to the Grub Street Verse-writers:

Lend these to paper-sparing Pope;

And when he sets to write,

No letter with an envelope

Could give him more delight.

We were getting there! People did use envelopes at that time though that was uncommon.

One century later, Porny's guide Models of Letters, in French and English (1797) was more explicit. Envelopes were not yet the norm, but they were a sign of respect (Porny, 1797):

It would be impolite to send a Letter without a Cover, to a Superior person; that may be done only with inferiors, and between equals that are familiar, and who, on this occasion, reciprocally excuse one another.

The book is written both in English and French: in the French version, the above text uses the word envelope for "Cover".

As for closing the letter, Porny made a distinction between the cheap wafer and sealing wax:

It is neglecting the respect due to a superior to seal a letter with a wafer, when we write to a person above ourselves. In such a case, sealing was is to be used: and this wax must be black, when the writer is in mourning.

Wafers at that time were made of flour paste mixed with egg white, other sticky ingredients like gelatin, and colouring. The mixture was cooked and it had to be moistened to be used, presumably by licking.

Thirty years later, François Peyre-Ferry, a French teacher in Connecticut, repeated this writing etiquette for American readers:

All letters written to persons of distinction, should be inclosed in an envelope of white paper, perfectly neat, and without any thing written or printed on the inside. The most simple manner of folding any other letter, so that its contents cannot be seen, is always the best. For sealing, use red Spanish wax, when neither you, nor your correspondent, is in mourning : in the two last cases, make use of black wax. Wafers may not be used, except in writing from equal to equal, or from a superior to an inferior.

Still, envelopes were still rare. In the UK and France, recipients paid postage on delivery, charged by the sheet, and on distance travelled. Adding a "cover" meant paying double postage. As a result, envelopes were "scarcely known beyond the limits of official departments, and the occasional use of them by those who possessed the privilege of franking" (Philbrick and Westoby, 1881, from whom what follows is derived). What made them popular was the reform of the British postal system in 1840 (in 1848 in France). In France, envelopes were impopular with businesses because one could not stamp the letter itself on departure and arrival (Maury, 1907). The invention of the modern prepaid postage stamp changed everything, and made envelopes possible (Philbrick and Westoby, 1881):

Gum was an article seldom heard of except in connection with pharmacy, for wafers and wax were the recognized means of closing letters so far as that was practicable, and were the regular appliances as well of the commercial desk as of the library table. But when it was permitted to enclose a letter in a cover without incurring the penalty of double postage, the facilities afforded by the use of envelopes and the privacy secured by enclosing correspondence in them soon produced their effects, and envelopes made their way into public favour so rapidly, that stationer after stationer set up workshops for the manufacture of them. Many stationers had patterns of their own, and registered their designs ; in short å new trade was created, which gave employment to hundreds of young people of both sexes. At first ornamental adhesive seals and enamelled wafers were commonly used for securing the flaps, but the greatest improvement was the lengthening of the upper flap and the gumming its extremity. From this period the sealing-wax trade began to suffer most perceptibly, and is possibly the only one which may be said to have been ruined by the introduction of the penny postage.

The "gum" was made of potato starch and was used both on stamps and envelopes. According to Harper's New Monthly Magazine (1852), it was discovered by accident after a potato starch factory went out in flames in 1821, and people who had carried buckets of water to extinguish the fire found that "clothes were gummed together".

In 1840, the year of the introduction of the "Penny Black" adhesive stamp, British inventor Edwin Hill took a patent for a machine for folding envelopes. The patent was bought by Warren De La Rue, and by 1845 La Rue was making envelopes at the rate of 2,000 per hour. They were first gummed by hand, but, at the Great Exhibition of 1851, La Rue demonstrated a fully automated machine that turned out "3,600 envelopes per hour, all folded with mechanical exactitude, and securely gummed." (Philbrick and Westoby, 1881)

An alternate reason for the sudden popularity of the envelope was proposed by a reader of the British scholarly journal Notes & Queries, who wrote in 1871:

I believe that the large 4to writing paper, capable of being folded so as to form a cover, was in common use in England until 1840, when, the weight of a letter carried for one penny being restricted to half an ounce, the 4to letter paper was gradually superseded by the 8vo note paper. The 8vo note paper had, however, this disadvantage — it could not be folded so as to ensure secrecy: a cover therefore became a necessity. Our ever-inventive neighbours — the French — sent us the thing we wanted, and made us a present of the name enveloppe.

In any case, in the late 1840s, British stationery catalogues started advertising the "newly invented adhesive envelopes", not only in the UK but also for instance in Canada (Chalmers catalogue, 1847). Competition was fierce: stationery manufacturer Jeremiah Smith publishing the following ad in 1847 (The House of Lords, 1847):

The demand for these Envelopes is so great, and they are now so highly appreciated, that several unprincipled persons are offering for sale a worthless imitation, and others are representing themselves to be "Agents for the sale of Smith's Patent Adhesive Envelope," whereas J. Smith has no appointed Agents.

The main selling point of the adhesive envelopes seems to have been their better security. A report on an exhibition at the Crystal Palace at Sydenham in 1854 noted that adhesive envelopes "offered full security for sending banknotes" (Le Droit, 1854). A few years later, another ad by J. Smith also underlined secrecy (Debrett's Illustrated Peerage, 1862):

The most secure, neatest, and best made that can be obtained. It is invaluable to all who have any regard to the secrecy of their correspondance, and is no dearer that the so-called "cheap" envelopes.

In what could be an early attempt at product placement, novelist Elisabeth Gaskell mentioned the secrecy allowed by these envelopes in her short story Uncle Peter (1853):

Her first proceeding, when she found herself there, was to lock the door; her next, to sit down and examine the exterior of the letter; but, thanks to the patent adhesive envelope, its contents were impenetrable even to her skilful manipulation.

But were gummed envelopes more resistant to prying eyes than wax-sealed ones? In 1870, France announced the shutting down of its cabinet noir, the "black chamber", the intelligence service that had been used since the 17th century to open (and reseal) private letters to look at their content. With hundreds of millions of letters circulating in France in the late 1870s, the cabinet noir was no longer suited to the task. In an article titled La sécurité des lettres (The safety of letters), the newspaper La Cloche reported on a experiment that showed that all letters were vulnerable: it took two minutes for a trained operator to open and close a gummed or wafer-sealed letter, four minutes for a simple wax-sealed letter and up to 12 minutes for a top-security letter (five wax seals linked by a metal wire): the operator removed the bank note inside without leaving any trace of snooping (Desonnaz, 1870).

In addition to adhesive envelopes, there were also new adhesive wafers made of paper, but they only lasted a decade and were no longer used after the 1860s (Champness and Trapnell, 1996).

By the 1850s, adhesive envelopes had been widely adopted, as notes an author in the American literary magazine Graham's Magazine (W.W., 1856):

The man of business uses an adhesive envelope; the old-fashioned tradesman still sticks to a wafer; the pompous man treats you to wax and his crest; the seal of the illiterate bears the impression of a button, a sixpence, a thimble, or a thumb.

In 1865, the English magazine Fun published the following joke:

Why is an adhesive envelope like a boy who doesn't know his lesson ? - Because it is licked and turned down.

But I've not yet mentioned the “ick factor”...