In late 1941, Britain was both the world’s largest empire and a nation fighting for survival. It ruled a quarter of the world’s land surface; its navy controlled the most critical sea lanes. Yet the resources on which its population depended to live and its armed forces depended to fight came from distant colonies and, increasingly, the U.S. The fleet that carried these supplies was highly vulnerable to German U-boats. Unlike its enemies in Europe and its potential Japanese antagonist in Asia, Britain faced having to fight across two continents and two giant oceans. To understand the complex and precarious position in which Britain found itself in late 1941, the first volume of Daniel Todman’s “Britain’s War” is essential reading. It ranges across the British Empire and is as attentive to social history and the lives of ordinary people as it is to high politics and grand strategy. As Mr. Todman details, from 1939 to 1941, “British strength determined, for the last time, the future of the world.” As the world descended into a “truly global war,” Britain, though still indispensable to the fight against the Axis, was forced to confront its loss of global pre-eminence, not to its enemies, but to its new superpower allies. Few books demonstrate the superfluousness of counterfactual “history” as well as this one does. The coauthors offer a gripping blow-by-blow of the five-day span between Pearl Harbor and Germany’s December 12, 1941, declaration of war on the United States. In retrospect, many parties to the larger conflict, particularly those taking the American side, have cast American participation in a multi-theater war against the Axis as inevitable. Through an intensive transatlantic search of relevant archives, the authors show this not to have been so, recreating all sides’ uncertainty at a fraught moment. Each for its own reasons, Great Britain, the Soviet Union, and Japan eagerly sought Germany’s entry into a shooting war with the United States. Debate reigned in Washington and Berlin on how to handle the putative foe.