Prescriptivists would say it should be "one [..] upon his", but the author may wish to avoid using gender specific pronouns and is thus using the singular "their" instead.
I accept both points. I was reflecting on usage I have seen in late Victorian/Edwardian sources. That seemed to fit with the style of the text (although not the visual presentation of the page).
PS: 'Spiffing' is later and the Jeeves references in the HTML markup point to 1920s. Biggles. Biplanes.
PS: 'Spiffing' is later and the Jeeves references in the HTML markup point to 1920s. Biggles. Biplanes.