Kinda hard to make out the actual size from those pictures, but it looks more like it was once a pretty nice rifle.
There is a strong possibility that it started life as a Rook Rifle, rooks being akin to our crows or magpies, here in North America, considered a pest and generally, shot at as a form of recreation, by the landowners, to the extent that there was a whole class of rifles collectively known as Rook Rifles. They fit roughly into about the same usage as we think of grabbing a 22 for.
In any case, to determine the caliber, a chamber casting, or at least a better look over at markings will be required. There were rather a lot of rook cartridges in both rimfire and center fire, and varying calibers, but .310 was fairly common.
The wire stock, was added some time after it was made, whether to use as a poachers gun, easily hidden (the 'fun' story), or simply as a bodge to get some more use out of a broken stock gun cheaply (more likely, but not as 'fun').
Someone once mounted at least one, maybe two different side mount scope bases on the barrel.
Not very sympathetically either.
It needs a good looking over for any other markings. Typically, if it was British made, there would be Proof House stamps at various points (do a search for "Proof Marks").
If you find a small oval or a Crown and the Letters ELG,, either alone or surrounded by a oval, it is a Belgian Proof Mark.
Anyways, it claims by the engraving to be made to Martini's Patent. Other markings will tell the rest.
I doubt it started as a Martini Henry, more like it was made to be what it was before several unsympathetic hands made it a lot rougher.
Cheers
Trev