I've seen claims of 10 rounds per minute for the USN 6in/47 triple turret and thus a 6 second firing cycle.Some of it depends on the range but the British cruisers look like they had about 75% of the fire rate of the Americans, which is not bad compared to 8in guns
US guns had power ramming up to 20 degrees and the British used had ramming, since everybody had to lower the guns to load/ram elevation/range had an influence on rate of fire.
Japanese 5.5s depended on how far the crews had to lug the shells.
Agano may have been at 5-6 rpm and the Oyodo was lucky to hit 5 rpm.
This is from Wikipedia regarding the Belfast and Fiji class 6in turrets:
"A RN gunnery officer on HMS Bermuda gave details of the loading cycle which could be attained in the Mk XXIII turret with a well trained crew: "...a loading cycle of four and a half to 5 seconds was attained at low elevation, another two to three seconds being required with the guns elevated for long range. The time would lengthen as fatigue set in, but was creditable..."[4 - Brook, Alarm Starboard]"