Rimmed rounds are not ideal for repeating rifles and automatic weapons. Britain had been trying to replace the .303 since the Boer War so why not share development costs with the French? No 1 basic design dates back to the late 1870's and needs replacing with something stronger. Otl this was the No 4 Mk1 that sat on the shelf for 10 years before entering mass production.
Rimmed cartridges work very well with repeating rifles and automatic weapons, as repeatedly proven by, not only, British, Soviets and Japanese.
Want to improve life for Johnny, the average infantryman, by improving his weapon? Introduce a reliable self-loading rifle, if not assault rifle by 1930s, all together with intermediate cartridge (whether something along the lines of .280 British, 6.5mm Arisaka, or perhaps a rimless '.303 Kurz').