For what it's worth, drafted this at the time, and meant to check it before posting, because I know how some on here like to pick holes
But kind of lost the will to live about it, and couldn't be bothered getting back to it, but thanks to Captain Cab for reminding me.
Not that it's any great shakes, but it did my head in thinking about it. For at least five minutes
So basically three different scenarios. In Leicestershire, for example:
HC and PH badges only, eg Blaby
Dual badges only, eg Oadby & Wigston
HC, PH and dual badges, eg Harborough
Maybe a fourth scenario in Hinckley & Bosworth, where there's no HC badges recorded, but there are PH and dual badges.
So the latter is maybe similar to the Scottish HC badges, which by default allow you to also drive PH. So they're effectively the same as a dual badge in England, but they're not described as such. However, a PH badge in Scotland allows you to drive PH only.