This week’s palaver in Britain over the economic effects of Brexit is a sideshow. While politicians, pundits and voters stage a largely meaningless freak-out over precisely how many percentage points leaving the European Union will shave off gross domestic product a decade from now, a worrying transformation is already under way: Britain is steadily turning into Japan.

Careful observers have noticed warning signs of Japanification for some time. Rapid and illogical currency devaluation—check. Rising protectionism—check. Hostility...