The Center for Human Rights in Iran, a New York-based advocacy group, said in a posting on its website that Ms. Amiri has been incarcerated in a wing of Tehran’s Evin Prison operated by the Intelligence Ministry, which is “holding her without access to a lawyer on national security charges.”

Without identifying Ms. Amiri by name, the British Council said, “We are aware that one of our staff has been detained in Iran while making a private family visit.”

The British Council also denied that she had traveled to Iran on its behalf. “This colleague does not travel to Iran for work,” it said in its mailed statement. “She works in the U.K. to support and showcase the Iranian contemporary art scene.”

At least one other Iranian with British connections arrested recently is a dual citizen of Britain and Iran. Abbas Edalat, an academic and antiwar activist, was arrested in mid-April, an Iranian judicial official confirmed last week. Mr. Edalat, a professor of computer science and mathematics at the Imperial College of London, had been invited to speak at an academic event in Tehran.

Image Abbas Edalat, a professor at the Imperial College of London, was arrested recently by Iranian intelligence. Credit... Imperial College of London

The fate of another British-Iranian dual citizen, Mahan Abedin, is somewhat murkier. A writer and analyst generally favorable to the Iranian government, Mr. Abedin failed to return as scheduled on April 29 from a visit with family in Iran, said his publisher, Michael Hurst. His only contact with Mr. Abedin, he said, has been a brief note saying he was “fine” and to “please stop contacting me.”

Iran Wire, a news website run by expatriate Iranian journalists, said on Monday that Mr. Abedin had been arrested on suspicion he conspired in an “infiltration” operation. Britain’s Foreign Office disputed that account.