Let's just hit the 'back-to-basic' button here for a moment, please, and stay with the handgun under discussion.

If the handgun fires a new load every time you squeeze the trigger, and only because YOU have squeezed the trigger, like an old-fashioned cap gun, then it is manually operated. It is legal, just as a six-shot Adams double-action percussion revolver is legally a Section 1 firearm.

If the handgun fires a new load because the energy of the propellant is somehow arranged to cock the handgun and advance the next load for firing at a subsequent squeeze of the trigger, then is is plainly a self-loading handgun, no matter that it is a nitro or black powder shooting firearm.

Note the wording in the description of the W-F revolver - 'The Webley–Fosbery Self-Cocking Automatic Revolver was an unusual, recoil-operated, automatic revolver.....'

Here on mainland UK, such firearms are the province of Section 7 category firearms.