A research group which aims to "strengthen" academic relations with the Middle East is managed by active supporters of the academic boycott.
LSE's Middle East Centre - a multidisciplinary research centre focusing on modern Middle Eastern cultures, societies, economies and international relations - opened in October.
Among its listed aims are strengthening relations between LSE and Middle East universities and increasing LSE's capability to engage with countries in the Middle East.
LSE academics Dr John Chalcraft and Professor Martha Mundy, both members of the British Committee for the Universities of Palestine (BRICUP), which calls for an academic boycott of Israel, are among the four academics in the management group.
Dr Chalcraft argued in favour of a boycott during last week's LSE debate, while Professor Mundy has written extensively in its support.
Another member of the management group is Professor John Sidel, a member of Independent Jewish Voices, which has taken highly critical views of Israel.
During last week's debate, Professor Daniel Hochhauser said: "I find it incredible that Dr Chalcraft is on the board of an organisation that exists to strengthen relations between LSE and the Middle East and yet he calls for a boycott of Israeli academics.
"It is very difficult to see how LSE's Middle East Centre could have even the minimal amount of academic credibility."
Jonathan Arkush of the Board of Deputies said: "By their membership of the centre's management group Dr Chalcraft and Professor Mundy are committed to promoting academic links between LSE and Israeli universities, which is welcome.
"People are entitled to ask them to put on record that they are therefore opposed to boycotting Israel and anywhere else. They cannot be both pro- and anti-boycott at the same time."
But defending his position during the debate, Dr Chalcraft said: "This is ok, especially in a liberal society. We are allowed to hold opinions that are not necessarily held by the corporate institutions for which we work. If we can't have that space for freedom, for dissent, then we're really in trouble."
Fawaz Gerges, director of the centre, said: "The Middle East Centre is committed to rigorous research and scholarship through the scrupulous preservation of its academic independence.
"There is a distinction between the policy of an institution and the views of individual academics, who retain their freedom of opinion. "
Last year, LSE apologised after an illustrative map accompanying a story about the new centre in its Connect magazine did not feature Israel, despite labelling Gaza and Beirut.