Citizenship lessons were central to addressing issues of segregation in today's society, the MPs added.
But the report's conclusions were not supported by Conservative members of the committee.
Subject to a review by academics at the Institute of Education at London University, the government should make school councils compulsory, the committee said.
"Well-run councils offer students opportunities both to participate in democratic, representative practices, such as elections, and to effect change in their school environments," the report said.
Pupils should be trained in negotiation, communication skills and leadership to help the school councils work well, the committee added.
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