So far as I could discern from my research, the muffin man was never a warning. IME, it was just a bit of doggerel a Drury Lane baker came up with to hawk his wares on London streets. So far as I could find, that Wikimedia Commons infographic is the earliest printed form of the rhyme. The form we knew as kids seems to have come even later than that printed version, near the end of the 1800s, maybe even into the early Edwardian period.

I just stumbled upon the horrors of Amelia Dyer while researching the urban legend around the origins of the original rhyme.

Contrary to popular belief, the muffin man rhyme was not part of the original Mother Goose book from the late 1600s. That too, IME, would seem to indicate the rhyme simply did not exist as far back as the 1500s when Linwood was rumored to have been murdering children and competitors.