UNDER DAVID Cameron’s leadership, Britain’s importance as a U.S. ally has steadily diminished. His government was slow in joining the campaign against the Islamic State and has played no significant role in resisting Russian aggression in Ukraine. Following a rebuff by Parliament, Mr. Cameron retreated from airstrikes against Syria in 2013, prompting a climbdown by President Obama that has had disastrous consequences. Mr. Cameron’s most notable foreign policy initiative was his craven courtship of Chinese dictator Xi Jinping in the hope of reaping commercial advantage.

Consequently, the result of Mr. Cameron’s last and most calamitous misstep, the promotion of an unnecessary referendum on Britain’s membership in the European Union, should logically lead to an acceleration of an existing trend in U.S. foreign relations, rather than an abrupt shift. As it already has, the Obama administration will look more to Germany for help and leadership on transatlantic security issues, while cultivating stronger strategic relations with Asian partners such as India and Japan. It should not expect much help from London in managing new crises in the Middle East and elsewhere in the coming years — but then, that was already pretty much the case.

How much further the “special relationship” between the United States and Britain will be devalued will depend on what now looks like a very unpredictable course of events in London.