Getting back to the original question, I have a BSA Martini Model 15 that was converted to .22 Hornet using the original .22 Long Rifle barrel prior to my acquiring it. It's the less common saw-handled stock, but is otherwise quite similar to RWTF's Model 12/15, except that the rear sight is actually mounted on a vertical dovetail at the rear of the action rather than separately on the tang.
The firing pin needed to be re-bushed, which was done by David Kaiser. Once that was done, I discovered it is a quite pleasant and more than satisfactorily accurate rifle. I have no idea how long the rifling in barrel will last with the higher temperatures and pressures of the Hornet compared to the Long Rifle, but I doubt I'll shoot it out in my lifetime.
The .222 requires a rimless extractor (Bob Snapp made them and may still, for all I know) or procurement of a batch of .222R cases.
As nearly as I can tell from 20 years of small frame Martini shooting, the BSA rimfires make quite satisfactory rimfires as long as the firing pin is bushed. Since you have to bush the Cadet firing pins as well for any of the higher pressure cartridges, starting with a rimfire is not really all that inconvenient. I've owned small frame Martini centerfires in .20-20 KCF (think .20 Mashburn Bee), .20 Tactical, .22 Hornet, .218 Bee, .218 Mashburn Bee, .219 Zipper, .222 Rimmed, .225 Winchester (which was loaded down a bit in view of the case diameter), .256 Winchester, .310 Cadet, and .357 Magnum, and I've probably left one or two out. I have an action set aside that will be a .30-30 or a 7x30 Waters if I ever get the funds and the ambition together simultaneously. They are fun little guns and deserve more respect than they get.