A Commonwealth fleet would require shared political command

Could a combined Commonwealth fleet have survived the end of the British Empire?

Possibly, but only with a combined command structure and corresponding shared political control, much like a formal alliance.

Ships and shipyards alone would not make a durable multinational fleet. Shared units require a combined command system and, behind it, a political mechanism able to decide when and how those forces operate. The answer turns an industrial counterfactual into an institutional problem resembling NATO.