A bit more reading revealed that in 1655 Cromwell’s head was superimposed on the earlier Charles I engraving. To the detriment of my “Charles I is Cromwell” theory, the Schama seems to have included the wrong engraving. The Cromwell version looks a bit more Cromwell-esque:

This turns out to be quite a remarkably interesting piece with a long and dubious history, and is nicknamed the “Headless Horseman.” The Folger Shakespeare Library has a bit on its history here, and a version of the engraving without a head at all is to be found here.

Perhaps it would be good business sense to make a large flat wooden cut-out of the scene, and cut a hole where the head ought to be. This would allow tourists to pose for photographs as a 17th century equestrian lord.