Mr. Farage’s success is both a symptom and a cause of the newly febrile mood in Britain. The turmoil of the past decade, with its succession of six prime ministers, had already stripped the country of its reputation for stable and competent government. Lately, things have felt wilder and more menacing. Last summer, anti-immigration riots broke out across the country, recalling the heyday of the National Front, and there have since been recurrent demonstrations outside hotels where people seeking asylum are housed. In September, over 100,000 far-right protesters gathered in London for “a free speech festival” organized by Tommy Robinson, a far-right extremist who has served multiple prison sentences.