In a letter to local authorities he has warned that there is no excuse for using "covert" admissions practices that exclude pupils from poorer families, such as requiring pupils to wear expensive uniforms.
The Office of the Schools Adjudicator is investigating 79 schools that are suspected of breaching admission rules that were introduced last year.
The government has introduced a revised appeals process for parents who believe they have been unfairly refused a place for their child.
Shadow schools minister Michael Gove said the solution to the problem is to create 200,000 more school places.
He added: "The answer to a failed status quo is not more bureaucratic meddling but welcoming more new schools into the state sector."
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