During the height of the Napoleon scare, 1803-1805, when the Camp de Boulogne was in full swing and Napoleon really seemed to be about to invade the British Isles, propaganda in Britain painted Napoleon as the devil incarnate. They called him Boney, which itself became corrupted to Bogey and Bogeyman, as the following nursery rhyme shows.
'Baby, baby, naught baby,
Hush! you squalling thing, I say;
Peace this instant! Peace! or maybe
Bonaparte will pass this way.
Baby, baby, he's a giant,
Black and tall as Rouen's steeple,
Sups and dines and lives reliant
Every day on naughty people.
Baby, baby, if he hears you
As he gallops past the house,
Limb from limb at once he'll tear you
Just as pussy tears a mouse.
And he'll beat you, beat you, beat you,
And he'll beat you all to pap:
And he'll eat you, eat you, eat you,
Gobble you, gobble you, snap! snap! snap!'
Source: Eliza Gutch and Mabel Peacock, County Folk-Lore, vol. 5: Examples of Printed Folk-Lore Concerning Lincolnshire (London: Folk-Lore Society, 1908), pp. 383-384.
Although it is an English lullaby, sometimes the name “Menshikoff” is used in place of Bonaparte. In another version of the poem, the ogre is named Wellington. Variants include “And he breakfasts, dines, rely on't” and “every morsel snap, snap, snap.” A Japanese website contends that this lullaby had been around since the early 1600s, using the names of Cromwell and Charles I as “ogres”. Be that as it may, ever since Napoleon, parents wishing to encourage recalcitrant children have threatened with the words 'The Bogeyman'll come and get you'.
Details courtesy of Elaine Hutchison, independent scholar