The Midland Gun Company originated in Birmingham, England in 1888. They made their own guns. The remnants of the company were bought by Parker Hale around 1956.
I suspect that what you have is an Italian made firearm imported and marketed by someone with the rights to the Midland name. Could be P-H, or someone else who later acquired the rights to the name.
You need to find out which Italian firm made the gun. It may have a maker's stamp on it, or you may have to do a lot of research. There are, and have been, many Italian gunmakers. Some were simply contractors in Val Trompia who accepted piecework from the local artisans and cobbled together guns. Others did a little better, eg. Beretta. It is possible that you will never find out who actually made it.
Since you say it is a sidelock, and that most of the internal parts are missing, it is unlikely that you will be able to fix it economically, if at all. Most of the internal parts of a sidelock ARE the sidelock, and each one has to be hand fitted by a skilled worker. The only other parts are the firing pins and the bolt. You will not find important sidelock parts at Numrich or Western Gun Parts. There are 2 or 3 gunsmiths in Canada who could make you the parts. Think mortgage.
Sorry to be the bearer of bad news, but based on your description I think you have a headache on your hands. Please post pictures anyway - Italian sidelocks are reasonably rare and usually fairly nice.
Sharptail