They are supposed to welcome all students, but a popular public high school in Melbourne has been accused of turning away poor children who live in public housing.

In an unusual intervention, Education Minister James Merlino forced Melbourne Girls' College to enrol 12 students it had initially rejected, including residents of the nearby North Richmond public housing estate.

The case highlights issues around the gentrification of public schools with booming enrolments and the impact on poorer students' access to a good education.

Richmond MP and Planning Minister Richard Wynne said he had fought with the school and Education Department for a decade to ensure students in nearby public housing were able to attend the popular school.