Mission command existed before navies named it

Did English-speaking navies only adopt mission command after the Second World War?

No. Commanders practiced it earlier; the postwar change was largely the naming and codification of behavior already present in operations.

During the Bismarck pursuit, dispersed task forces maintained radio silence and sometimes disregarded unsuitable directions because local commanders understood that their authority included acting on the mission rather than obeying every signal literally. This practice predates the appearance of its modern label. Vian, Dalrymple-Hamilton, and other Royal Navy commanders already exercised initiative within broad intent, even when no one called it mission command. Later codification mattered because it converted an inherited habit into doctrine that could survive peacetime turnover and enter institutional memory.