In a lecture this week at the Institute of Education, Mr Hirsch says privilege in education is now more than ever related to where you live. Places at popular schools are often only available to children of a privileged elite because of the tendency for affluent families to cluster in particular areas.
He suggests attempts could be made to construct admission criteria that would mean comprehensives take a wider spread of ability and a mix of children from deprived and advantaged backgrounds.
Despite the Government's introduction of open enrolment, research by the National Foundation for Educational Research shows that catchment areas are the single most important factor when over-subscribed schools select pupils.
According to Mr Hirsch, it might be possible to avoid the situation where more advantaged children tend to have a better chance of getting into a "popular" school. Before the abolition of the Inner London Education Authority, for example, schools in the capital were required to take children from three ability bands, measured by a reading test.
The other example is city technology colleges. These schools are required by law to have intakes that span the whole ability range. (Mr Hirsch points out that the criterion can be undermined through interviews to select the best-motivated applicants.) It might be fairer, he suggests, for schools to have wider catchment areas and select their intake at random rather than from those living closest. Another option might be to allocate a fixed proportion of places by random ballot.
Mr Hirsch also advocates the creation of a national application system covering grant-maintained, local education authority and church schools, similar to the Universities and Colleges Admissions Service system for admitting students to university.
The agency would be independent of local authorities and the Funding Agency for Schools. Such a system would require the Government to set clear principles for selection and parents to receive some guarantee of a geographically accessible school. Unless the problem is tackled, says Mr Hirsch, the system is likely to grow more polarised between privileged and disadvantaged groups.
Donald Hirsch, author of School, a Matter of Choice: a study of choice in six countries, is a visiting fellow of the London Institute of Education.