The challenge has been issued by the Association of School and College Leaders (ASCL) and Foundation and Aided Schools National Association (FASNA).
ASCL leader John Dunford said those who did not get in to the more desirable schools in England felt hard done by.
Letters about secondary school allocation are being sent out later.
Meanwhile, a parental advice charity has begun a text message service on how to appeal.
The admissions regulator, chief schools adjudicator Philip Hunter, has said that the present system of admissions and "parental choice" is fuelling social and racial divisions.
He has said that options that will be unpopular with many parents, such as having local lotteries for places, might be necessary.
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