A team of three journalists, which included reporter John Sweeney, travelled to North Korea last month with members of a London School of Economics (LSE) student society.
The LSE has said the genuine students on the trip had been "deliberately misled" by the BBC and were put in "serious danger" by the presence of the BBC team, The Telegraph reported.
The BBC said the students were told a journalist was among the group and warned of the risks.
"At no point prior to the trip was it made clear to the students that a BBC team of three had planned to use the trip as cover for a major documentary to be shown on Panorama," the LSE said in a letter to all members of the university.
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The LSE has accused BBC of taking an "unacceptable" risk.
Had the journalists' identity been discovered by the North Korean authorities, the entire group could have been arrested and faced punishment.
The journalists travelled to the country with members of the LSE's Grimshaw Club, which was established in 1923 and is part of the International Relations Department.
While in North Korea, the Panorama team filmed undercover footage that will be broadcast in North Korea Undercover tomorrow.
The LSE has demanded the BBC withdraw tomorrow's Panorama programme about North Korea.
This weekend, LSE officials sent a letter to all members of the university, deploring the tactics used by the BBC to get its journalists into North Korea which is at the centre of international focus for its nuclear threat.
"The School wishes to alert all staff and students to a serious development which may affect them personally in future. This relates to the conduct of the BBC in respect of a Panorama programme entitled North Korea Undercover, which is due to be shown next Monday evening, April 15," it said in the letter.