From "With British Snipers to the Reich", by Captain C. Shore
" I used a good deal of American .303 (particularly WRA) and this gave consistently fine shooting ."
WRA = Winchester Repeating Arms Company - New Haven, Connecticut. Manufactured .30-'06 Springfield and .303 British ammunition during World War I and World War II.
It is very very unlikely that any interwar stocks of .303 ammunition would have existed in 1944. What hadn't been used or abandoned by the BEF in France, would probably have been used in training, with newly made .303 being issued to the front line.