Cordite was used for rifle caliber ammunition by the U.K. at least through WWII, though production shortfalls caused the widespread use of other propellants by the Brits for rifle ammunition in both world wars. I, quite a while back, purchased some 1930s Kynoch commercial Mk VII ball ammunition and military Kynoch Mk VII ball from the mid '40s. I pulled the bullets from both lots to use in reloads as there were hangfires with them and all of them were indeed loaded with cordite. If Mk VII ammunition is not loaded with cordite it usually has a suffix behind the VII like a "z," at least until the late 1930s - mid 1940s when cordite was largely, but not completely, replaced for small arms use and the suffix was generally thought unnecessary. I actually found some Yugoslav manufactured ammo headstamped Mk VIIz produced in the late 1960s, very high quality stuff.
By the end of WWI cordite's real niche was as an artillery propellant and sometimes rocket fuel. These uses undoubtedly contributed to the shortages for rifle and machine gun ammunition. The last U.K. factory producing cordite closed less than 20 ago so it was around for a long, long time after its use as a rifle propellant ended.