The one Sedgley Hornet I worked on (was more than a couple years ago) was on a regular full length 30cal '03 action.
The magazine was a rather crude looking thing made of separate sheet metal pieces to form a box. Seems like it had a separate ejector attached to the magazine assembly but I may be wrong on that.
Bolt face was reduced in size and re-machined for the hornet and the extractor hook lengthened IIRC.
The bolt throw was shortened to about what the pic posted shows.

Dispite the kind of crude appearence of the internal part of the conversion, it worked very smoothly.

I don't remember how it was ser#'d. The couple of Sedgleys I've had and the one I now own have a 'new' ser# in the sear channel in the rear tang. The front recv;r ring having been ground off,,,. I think the Sedgley proof mark is a S in a circle but I haven't had a look at it in a while.
Bbls are usually marked with the Sedgely name.