What is the origin of being "in the pudding club"?

I can't tell you whether it's used today, but it was still current in 1976. I'm watching a rerun of a British sitcom (originally aired in May 1976) in which the phrase was used; the character who used it, and the two who understood it, are urban (London), are lower-middle class economically, and are middle-class in outlook (they value outward respectability and the upholding of middle-class social norms).

In the 1828 AMERICAN DICTIONARY OF THE ENGLISH LANGUAGE you can read definitions for pudding: "what bulges out, a paunch." So a pregnant woman had a "bulge" for her tummy same as a "paunch."

I was just watching "Last Tango in Halifax," a British sitcom, and the phrase "he put her in the pudding club" was used as it if was commonly understood.

It wasn't merely a sexual reference; more of a play on words since there used to be (and still are in a few places) Christmas clubs, in which everyone paid a small amount each week and received a hamper at Christmas, and bottle clubs, in which the reward for your subscription was a bottle of whisky. So presumably the lady in question had received a package as a result of her efforts...

And the shortened version, in the club, is still used in Britain (or in London, at least). I would advise caution, since it is very colloquial bordering on the vulgar; but I would think it would be understood everywhere.

I assume that "pudding" comes from the French "boudin". "Boudin noir" is the French for black pudding (there's also "boudin blanc" for Weisswurst). Pudding therefore means "sausage" - hence the seventeenth-century meaning of "penis"

“The Hasty Pudding Club” was also a social club at Harvard. According to the Wikipedia page, the (social) club was founded in 1795.

When my late mother was working in the local cotton mill before the NHS was formed, she was told she'd need to join 'the pudding club' when she became pregnant. It was a savings club for saving to cover the cost of the Dr & Midwife etc for the delivery of their baby.

The earliest mention I can find of the phrase is this brief entry in Albert Barrère & Charles Leland, A Dictionary of Slang, Jargon & Cant, volume 2 (1890):

Pudding club (popular), a woman in the family way is said to be in the pudding club.

Twelve years later, John Farmer & William Henley, Slang and Its Analogues Past and Present, volume 5 (1902) has this brief equivalence:

IN THE PUDDING CLUB (or WITH A BELLY-FUL OF MARROW PUDDING) = pregnant.

The phrase "in the pudding club" may have been popular by 1890, but it doesn't leave much of a mark in publications of the late nineteenth century. An Elephind search returns more than 150 matches for "pudding club" in U.S. newspapers prior to 1890, but all of them refer to the Hasty Pudding Club at Harvard University in Boston. This was a social club for Harvard students who met weekly and (at least originally) marked the occasion by eating pudding together.

In Britain, however, "pudding club" had a different meaning in the mid-nineteenth century. From John Oxenford, "The Grocer's Shop on Christmas Eve," in the Illustrated London News (Christmas 1850):

Pursued to all its ramifications, the pudding is still symbolical. In some neighbourhoods—not the most aristocratic—the investigator into life will find notifications of the existence of a "pudding club," rendered conspicuous by a coloured portraiture of the object. This picture, which will often be found in the grocers' shops of the suburbs, is founded somewhat on the principle of exaggeration. The pudding, which is to be the prize of the clubbist, is of enormous dimensions. Children, with rose-pink cheeks, are shown in attitudes of exaltation at its appearance; and the words that visibly flow from their mother's lips explain to the pater familias the advantage of pudding-clubs in general: but still one looks uneasily at the pictorial display, and cannot help thinking that if the pudding rolls from its plate—a very likely occurrence—the whole family will be smothered as by an avalanche.

Our more opulent readers, probably, do not know what a "pudding club" really is. It is a type of the reckless generosity and hospitality of our humbler classes, and therefore we have referred to it in illustration of our statement, that the pudding is symbolical throughout. Properly speaking, there is no club at all. The several subscribers pay a trifling amount per week, for a certain length of time, before Christmas Day; and when the total sum paid equals the value of materials for a pudding these are duly delivered. The political economist naturally asks, "What is the use of this payment beforehand?" The tally system—a grand destroyer of the well-being of of our humbler classes—is at once intelligible. The article of dress is taken first, and the instalments are paid afterwards: the purchaser securing the object of his wishes without ready money; and the vendor repaying himself for the absence of ready money by the largeness of his price. But the pudding-club is no result of a commercial principle; it takes root in a national sentimental peculiarity.

The peculiarity is this: the humbler classes of London cannot keep their own money. The stringent resolution to "put by" sixpence a week, backed by the most ingenious money-box, would break down before some call for the moment—a call probably arising not from a love of self, but from a good feeling for others. The visit of an old friend must be celebrated by a social glass—the distress of an unlucky neighbour must be immediately relieved—and how are these ends to be accomplished except by an attack on the reserved fund. With the humbler classes, there are, fortunately, always old friends, and, unfortunately, always unlucky neighbours; and, in the face of such a system, how could the amount required for the plum-pudding be ever raised, if the money were kept at home? The household god of the London family would ever be incensed at the absence of his proper offering. But the grocer, who institutes the the so-called "pudding-club," officiates as banker. The man who cannot trust himself with money, pays it away in the form of a subscription; and thus it accumulates, in spite of generous impulses, till the proper sum is raised. Is not this a great national fact, that our hard-working people of the humbler ranks require a check upon their impulsive generosity, even when the enjoyment of the one general holiday in the long, long year is the premium offered for a little frugality.

"Christmas in Whitechapel: Mr. Wilkins's Pudding Club," in London Society (Christmas 1863) gives a very detailed account of a pudding club in Whitechapel, including when that year's club commenced (in August), how much subscribers committed to pay (threepence or sixpence per week), and what the yield at Christmas would be (oranges, currants, candied peel, allspice, nutmeg, moist and lump sugar, tea, and coffee).

These clubs evidently had some staying power, too. The first notice of them in British newspapers held in the British Newspaper Archive appears in "Seasonable Benevolence," in the London Globe (December 25, 1846) [combined snippets], in the context of similar clubs dedicated to buying holiday geese and gin:

Christmas Dinner Clubs Experienced salesmen at Leadenhall-market state that the demand for Christmas geese has this year exceeded that of any previous season, and that the establishment of of clubs has, within the last few days, brought upwards of 20,000 geese into the market. The plan is for a certain number of subscribers to a club to pay sixpence or a shilling per week, for some time previous to Christmas day, to receive a goose and bottle of spirits. The publican holding the club generally enters into a contract for geese some months before, proportionate in number to his anticipated demand, and each vies in producing birds of the largest size and best breed. It has been stated that, from this competition, the quality of geese been much improved, from the greater attention which the extra demand has caused to paid to the feeding and fattening the birds. In some parts of the metropolis "plum-pudding clubs" have been established.

Pudding clubs were still active in London (and presumably elsewhere) at least as late as 1883, when a local newspaper reported a case involving the interception of an eight-year-old child who was trying to convey 2 shillings from his mother to "the grocer's pudding club." From "Police Intelligence," in the London Morning Post (December 12, 1883) [combined snippets]:

Henry Messenger, an intelligent lad, said that on the morning of the 24th ult. his mother gave him the sum of 2s. to take to the grocer's pudding club in the St. Jamess-road, Bermondsey. While proceeding in that direction the prisoner came up to him and stopped him. She took the 2s. from his hand and gave him a halfpenny.

Mentions of pudding clubs appear thereafter as late as 1900, but by then the heyday of the clubs was over. Still, a run of half a century is nothing to sneeze at.

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Conclusions

I think it is highly likely that the expression "in the pudding club" for pregnant arose, in the first place (albeit jocularly), in connection with the Christmas pudding clubs that grocers set up in working-class neighborhoods of London—and subsequently elsewhere in Britain from the mid-1840s to the end of the century. The association of pudding clubs with what John Oxenford repeatedly calls "our humbler classes" suggests that the term arose in that milieu.

Perhaps the notion was that, physiologically, the expectant mother was putting a little something aside each week for her gestating child, or perhaps the idea was that she was herself beginning to resemble someone who had eaten (as Farmer & Henley puts it) "a bellyful of marrow pudding." It is even possible that some survival of the old naughty meaning of "pudding" as sexual intercourse, sexual organs, or the like survived from the early 1700s and helped inform the usage.

That last possibility, however, strikes me as being rather unlikely, as (for example) John Hotten, The Slang Dictionary (1874), published just 16 years before Barrère & Leland describe the expression "in the pudding club" as "popular," not only doesn't have an entry for that expression but doesn't have an entry for "pudding" in its late seventeenth- and early eighteenth-century sense either. In fact, the only pudding-related entry Hotten offers is this one:

Pudding-snammer, one who robs a cook-shop.

Farmer & Henley, an encyclopedic reference work that is not at all shy about detailing slang related to what it calls "venery," cites only two instances of "pudding" in the sense of coition or the penis—one from 1682 (noted in Robusto's answer) and one from 1719. Both are a long way from 1890.

On balance, it seems to me that "in the pudding club" is more likely to have originated in a G-rated sense comparable to today's "a bun in the oven" than in an allusion to "pudding" as an explicitly sexual activity or organ.