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During a House of Commons debate, the prime minister told a female Labor member to “calm down, dear.” In another debate, he told one of his fellow Conservatives that she was “clearly frustrated,” a comment perceived by many as sexual innuendo.

Those gaffes followed controversy in the summer over revelations about the prime minister’s relationship with senior executives at News International, the British arm of Rupert Murdoch’s News Corp.

Soon afterward, street riots erupted in British cities, and Mr. Cameron was criticized for not returning from his vacation early enough to deal with the crisis.