Not so for the British bombers with the Frazer-Nash or Boulton-Paul turrets
Pop see
here
The Lancaster, Halifax and Stirling had their ammunition (up to 10,000 rounds of it) for the rear turrets on tracks which fed into the turret. I'm still Googling but suspect that it was fed into a magazine which moved with the turret.
I wish I'd paid more attention when I went to the Air Gunnery display at the YAM in Elvington.