LONDON — After dismissing her defense secretary on accusations he leaked sensitive information, Prime Minister Theresa May of Britain declared the matter “closed,” and on Thursday her government insisted that the police need not investigate one of the most serious security breaches in recent memory.

But the former defense secretary, Gavin Williamson, is not going quietly. In interviews with Sky News and others, he was quoted as having sworn “on his children’s life” that he was not the source of the leak from the National Security Council reported in a Daily Telegraph article. He has demanded a police inquiry to vindicate him and accused one of the country’s top civil servants of having conducted a vendetta.

His protestations of innocence have raised questions not only about Mrs. May’s notoriously leaky cabinet, but also about how information is traded between Britain’s top politicians and its leading journalists and the nature of a leak.

Mr. Williamson has not denied reports that he spoke by phone to the author of the article, the Daily Telegraph’s deputy political editor, Steven Swinford, for 11 minutes on the day of the leak — apparently the main evidence against him. Instead, Mr. Williamson seems to be arguing that the conversation was not responsible for the leak that has cost his job.