The North London Collegiate School and its public relations firm have not denied reports in the Mail on Sunday newspaper that a teacher told a Jewish student she would be sent to "one of your gas chambers" if she did not behave.
The school says it has sought legal advice and taken "appropriate action" after receiving reports of an "offensive statement" made by a staff member.
The paper said the student was reprimanded after she cut to the front of a cafeteria line.
Tim Toulmin, the company's founder, told the Associated Press he would not discuss the "appropriate action" taken by the school and would not discuss whether the staff member involved had faced any disciplinary action. He said the school's administrators also would not discuss the matter.
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The incident was reported to the Community Security Trust, an advocacy group that seeks to protect Britain's Jewish community from anti-Semitic attacks.
Spokesman Mark Gardner said the group is working toward a resolution of the incident.
The school enjoys an excellent academic reputation and has been attended by a number of prominent figures, including American Vogue editor Anna Wintour and Academy Award-winning actress Rachel Weisz.