HBO pioneered them, starting with Robert Klein in 1975. That did that because stand-up was already super popular.
You have to be careful not to conflate the popularity of long form comedic monologues with the popularity of the long playing record album. Millions of people were listening to the former long before the 1950s through the medium of radio. For that matter Will Rogers released several popular records in the 20s and 30s.
I thought I had included this in my post, but I guess I dropped it as the post was getting too long.
I decided not to count the opening monologues that multiple radio show hosts did as stand-up because those were just a small part of a larger show. No question that a comedian’s monologue is similar to stand-up, but it was also similar to their vaudeville acts. Virtually all the top comics of radio got there through the stage and most simply continued their acts and their personas on their radio shows. Structurally, a monologue is a piece of a larger whole, not a performance on its own.
As far as I can tell, Rogers only released a few recordings in 1923. All were short pieces, two to three minutes long. None can be classified as a performance. He also appeared on some recordings of radio appearances, where he was one of the acts.
He wasn’t the only one to release short bits of comedy on records in the pre-war period. I won’t try to guess who was first. The same objection applies to them all: they were distinctly different from the comedy albums that started appearing in the 1950s that tried to emulate the feeling of attending a nightclub and getting the live act.
Yes, and music halls in the UK had comedians too. Some of them included musical interludes, but for some the main part of the act (one example is George Formby Sr) was mostly patter and jokes, with songs as only part of the act:
I guess that might be a little different to what we think of as stand up comedy these days though, same as American vaudeville. (I’m not sure why Miller’s cite, which is otherwise interesting, claims in its headline that stand up is a particularly American phenomenon - it’s been huge in the UK for just as long as in the US).
The more modern type of stand up comedy was certainly common by the 1950s. Spike Milligan and other members of the Goon Show had a famous radio show, which then moved to TV, but they had all started out live. Footlights, the drama society at the University of Cambridge, featured large amounts of stand-up comedy from early on, and launched the careers of half of British comedy through most of the 20th century.
The time when it becomes easy to think of lots of people who are clearly stand-up comedians in either the US or UK is the early 60s, I’d say.
The Goons and the Oxbridge crowd mostly did sketch comedy, though, rather than stand-up, although the line between can be fuzzy at times. Dudley Moore and Peter Cook, say, worked in the same vein as the Americans Mike Nichols and Elaine May. I’d call both sketch comedy but you seem to define it differently.
An excellent resource for learning more about this topic is The Comedians: Drunks, Thieves, Scoundrels and the History of American Comedy by comedy historian Kliph Nesteroff.
I cannot recommend it strongly enough.