The most popular such magazine at this time was True Story, a "confessional" magazine published by Bernarr Macfadden with a US circulation well into the low millions. It had a British edition that was widely available and would fit your criteria.

I described the contents of this genre in a recent article in this way:

The real breakthrough came in 1919 when, noting the popularity of the first-person stories of triumph over adversity sent in by readers of his fitness title, [Macfadden] launched True Story, a magazine comprised entirely of such stories, which became the publishing sensation of the next two decades. A compelling mix of sex, sin and redemption, covering hitherto barley mentionable topics such as illegitimacy, adultery, unemployment and crime (a mix readily satirised by critics as “I’m ruined!” journalism), the magazine peaked with sales in excess of 2 million copies a month, made Macfadden’s fortune, and received, its proud proprietor claimed, in excess of 70,000 submissions from readers every year.

Macfadden and his rivals were all quick to see potential in True Story, and numerous spin-off titles launched – True Romance, True Confession, True Detective and, eventually, both Ghost Stories and the short-lived True Strange Stories, born and died in the year of the Wall Street Crash, 1929. All shared the formula honed by True Story – a mix Macfadden himself liked to call “the folk literature of the common people of America” but that his critics denounced as trash: its subjects sinned, suffered and repented, eventually finding redemption (except in Ghost Stories, where, as Will Murray sagely notes, they died, dematerialised and repented). For Jacqueline Hatton, though – a scholar who wrote a PhD thesis on Macfadden’s publishing empire – something much stranger and more remarkable was going on:

"The relationship between truth and reality in True Story is too complex to be reduced to a yes/no question… The true/false conundrum is unresolvable, and indeed pretty much irrelevant, because the concept of truth itself was highly ambiguous in True Story. [It] inscribed truisms rather than truths, beliefs rather than realities."

Or, as Macfadden was said to have observed – in terms that have a very current resonance – if a story merely sounded true, it was true enough for him.

Mike Dash, "Fake news and Macfadden," Fortean Times 352 (April 2017)