@Sash got it right. At least some, maybe all, British produced Mk VII standard ball ammo used Cordite until the end of its production life. There were 'z' (non-Cordite) 303s - some in other marks that needed a denser chopped nitrocellulose; or a cooler burning powder for high round-count use in automatic weapons; or were standard Mk VII ballistics but loaded in North America with their powders including US Lend-Lease supplies. One of these interesting historical footnotes is that the very popular Hodgdon BL-C(2) powder started out as a Mk VIIz propellant. The Olin Corporation's Winchester-Western ammunition division was completing a huge Mk VIIz Lend-Lease order at the end of WW2 which HMG promptly cancelled. They were demilled and B.E. Hodgdon bought the powder calling it 'Ball Lot C'. As WW had a trademark hold on the word 'ball' for propellants, Hodgdon renamed it BL-C and it was a huge hit with his customers. When the surplus 303 powder was used, Olin produced a replacement in the form of the powder that derived from that old 303 propellant and adopted as part of its contracted T65 development work for the US Army which in turn became the 7.62mm Nato cartridge. Initially at any rate (things may have changed over 70 years), the new grade, renamed H. BL-C(2), was as per Olin's 7.62 M180 ball cartridge powder, but with the flash suppressant coating omitted.
The 280 British was chopped nitrocellulose from day one, hence its designation as Rifle Cartridge 7mm No.1z during its brief period of official adoption at the tail-end period of the post-war Labour Attlee government (in the face of fierce opposition from the USA and threatening to derail the creation of NATO as a military entity as the US were insisting on a 30-cal design, in effect their T65E3). Cordite would have been very unsuitable for such a cartridge design - not in its burn characteristics but from a manufacturing point of view. The workload in manually creating bundles of cords and inserting them into the case would have become prohibitively expensive by the 1950s and slowed production levels. Moreover, smaller calibre cases like the 303, never mind a 7mm, couldn't have the neck and shoulder formed until after the propellant bundle was inserted. That in turn proscribed final heat-annealing for obvious reasons (why very old Cordite 303 rounds often have neck-splits or incipient splits after long-term storage even in sealed canisters and a proper environment.)
The Kynoch etc big-bore African DG rimmed cartridges that someone mentions were designed for Cordite and the set-up was a part of their success. A Cordite bundle in a way over-size case left lots of airspace between the brass case walls and the propellant and reduced the effects of external super-heating in the African sun. When loaded for magazine rifles the really heavy hitters have to use tubular powders with heavily compressed charges with full power loadings to avoid recoil driving bullets back into the case for the unused rounds held in the magazine.
AFAIK only the British empire used Cordite as we know it - ie bundles of near case-length sticks or rods. Everybody else used chopped or cut powders, ie squares cut from thin rolled sheets or the extruded form chopped into short lengths by a spinning blade attached to the extruder. Ball powders date later from the 1930s when they were developed by Olin's Winchester-Western division whose production methodology was heavily patent-protected. Extruded / chopped etc were obviously much easier to mechanically meter and machine-charge cases compared to manually handled Cordite bundles. I can't imagine how many women were employed in British ammunition factories to create the bundles and charge cases with them manually especially during WW2. (Health & Safety must have been tricky too - nasty stuff in all sorts of ways to be handled for 40-plus hours per week!) Other people used very high nitroglycerin percentages in the mix too just like pre Mk VII 303 Cordite, but also like us learned how quickly they wore barrels. By WW2, the then current Cordite was nevertheless still much higher in nitro-glycerine compared to others, and the Americans had by then moved onto single-based grades typified by the surviving IMR grades such as 3031, 4064 and 4895.