Mark Twain probably didn’t make the famous quip, “History doesn’t repeat itself but it rhymes,” but the phrase’s sentiment often feels right. In discussing British independence, U.S. nuclear policy, strategic-weapons upgrades and a fraying “special relationship,” we could be discussing current events—or those of a half-century ago. In the late 1950s, Britain’s defense establishment faced some grim realities. The empire and its wealth were no more, and nuclear weapons were very costly. Although UK scientists played major roles in the Manhattan Project, postwar espionage and U.S. mistrust of the British led to a chill in collaboration and to the UK’s...