Why British cruiser guns split into three calibres

Did earlier protected and armoured cruisers directly determine Britain's later 6-, 7.5-, and 9.2-inch cruiser guns?

Not by themselves: manual shell handling favored 6 inches, while First Lord and First Sea Lord preferences helped select 7.5 and 9.2 inches.

A 6-inch shell was about the largest that could be handled by hand, reducing dependence on mechanical handling. The 7.5-inch choice is associated with the preference of the First Lord then in office. The 9.2-inch choice is associated with the First Sea Lord. Earlier protected- and armoured-cruiser experience alone therefore does not explain the later calibre choices.