It says that this practice is not new, but the fact that academies have autonomy over their admissions has "attracted controversy and fuelled concerns that the growth of academies may entrench rather than mitigate social inequalities".
The Commission said it had heard examples of some academies "willing to take a 'low road' approach to school improvement by manipulating admissions rather than by exercising strong leadership".
Under the current system, all state schools must abide by an admissions code, which says they must admit pupils in a fair and reasonable way. But the Commission's report said it had received numerous submissions suggesting that "academies are finding methods to select covertly".
Schools and academies can ask prospective families to fill in a supplementary information form (SIF) when making an application for a place. The report says that research shows that some schools, particularly those in charge of their own admissions, were asking for parents to fill in lengthy forms, involving open questions, and sometimes asking for information not allowed under the admissions code.
"Such practices can enable schools to select pupils from more privileged families where parents have the requisite cultural capital to complete the SIF in ways that will increase their child's chances," the report said.