I don't know who made the op's shot gun, but I'll offer up a couple observations.
The Whitworth markings on the bottom of the tubes of the OP gun look as they should. By that I mean to say that the
Trade Mark is deeply stamp into the steel. It was likely done (IMO) when the bbl was still in a rough bored state as the marking is so very deep and done with a single marking stamp.
To do that deep of a mark on a finished or nearly so tube will dent the tube. Gun fakers found that out and it's an easy way to spot those.
Maybe a mandrel was placed inside the bore at that spot to do those markings and then the final reaming was done after the marking.
The other thing is that the 'Sir Joseph Whitworth......' marking is a roll stamp marking.
Also quite deep but many have lost some depth from final finishing. Their placement on the tube is in a position where most can't be hand engraved into that location with any sort of ease and come out looking like a
decent roll marking. In other words to do this marking aftermarket, it has to be done by hand and in a position that is favorable to hand engraving.
Roll marking can be done, but on a completed bbl assembly, the bbl flats, forearm hanger get in the way.
Plus the bbl wall is thin, so the extreme depth of the orig markings can't be easily duplicated w/o them damaging the inner bore surface.
On the pics that Raimey posted of the barrels with the Whitworth markings,,those first two examples are hand cut (engraver) lettered.
The lettering is easily seen as being done by hand. Letters don't match one tube compared to the other.
The layouts are placed where it was easiest to do them by hand engraving,,not that they couldn't have been placed there originally. But again it's simple to see that they are hand cut.
The Whitworth 'Trade Mark' on the first one is a simple attempt to cut it in by hand engraving and using some punches to replicate the true trademarking. But it's not even close.
One thing that does stand out is that where they did plant the 'Trade Mark', there is a shallow but defined depression in the bbl wall.
That brings to question of wether either the attempt was made to stamp a trademark in that spot but failed (the bbl is springy and doesn't stamp easily especially when trying for the depth needed).
So that attempt was removed and what you see was added.
Or.. there was another Mark there of some sort, removed and the Whitworth trade mark put into place.
I don't think a Whitworth Trade Mark was there and then removed and the lettering recut. Why remove the vestige of what you would eventually want to put back there?
On the second example there was some sort of a figure/symbol in the position that the TradeMArk would have been.
About the 7 or 8 oclock position on the upper tube (LH tube) you can see what looks like the ends of (I'll call it ) Lobes for lack of any other word.
Doesn't strike me as part of the Whitworth TradeMArk,,but ..
Those Belgian guys made some nice guns...