Being "in the pudding club" seems to mean "being pregnant" in British English.
What is the origin/etymology of this phrase? Where is it used nowadays?
Partridge's A Dictionary of Slang and Unconventional English gives this entry:
That entry (interior emphasis my own) leads us to pudding, entry 2:
So it comes from pudding in the sexual, coital sense given above.
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).