How dangerous would a British-Soviet-American Cold War be without NATO or the United Nations?
Short answerIt would still be dangerous, but a Commonwealth forum and perhaps the League could provide limited structure while the great powers relied mainly on proxy conflicts and balance-of-power practice.
NotesThis counterfactual imagines the Commonwealth developing a broader forum that could admit states without the monarch as head of state. The League of Nations might also survive, though it would remain weak and divided between British and Soviet blocs. Britain and Russia would be expected to fall back on centuries of experience balancing one another through competition short of direct war. The result resembles the historical Cold War in producing messy proxy conflicts and few direct confrontations, with Ireland identified as one possible flashpoint.