Juno44 - please check your measurements again. For example, on the “Bottom one” you show a base diameter of 14.40 mm. However, for the same cartridge you show a rim diameter of only 13.43 mm. However, in the picture, this cartridge clearly has a larger rim diameter than its base diameter. Something wrong here, and that could be one reason no one has made any real identification.
The cartridge with the 13.43 mm Rim diameter appears to me to be a Cartridge Small Arms Blank, .303 inch MARK l, to use a British designation. The case length of these rounds ran between 38 mm and 42 mm. Of course, with a blank, although suitable only for inserting directly into the rifle’s chamber, and NOT suitable for feeding from the weapon’s magazine. The Mark l blank was approved for Land and Naval service in February of 1890. In March of 1893 the designation was changed to “Cartridge SA Blank .303 inch Black powder without Bullet Mark l (rolled case).” At the same time it was also declared obsolete.
Reference: “.303 Inch,” Chapter 8, Page 166, by Peter Labbett and Freddy Mead.
These rounds were charged with 34 grains of black powder and had a felt over-powder wad inside the mouth of the cartridge.
The other blank is very close in size, but larger, and I can find no reference for it that matches. It is too small to be a .577/.450 Martini Rifle blank, it seems.