Speaking at the union's annual conference, Andy Ballard told delegates that inequalities between different types of school foster inequalities between pupils.
There are too many different types of schools, such as academies, faith and trust schools, he said.
"More and more diversity of provision seems to be the order of the day, and this favours those with the cultural or economic capacity to compete for, and win, places for their children," he said.
He warned that looked-after children are particularly disadvantaged by the system.
He said: "With no family to join the bitter battle to get them into the most successful schools, they will be left with the worst choice. No wonder that their educational and life chances remain so tragically poor."
Ballard also claimed that private providers are damaging education standards.
"Too add insult to injury, this diverse provision is being handed to a wide range of unaccountable and undemocratic providers, a term better used to describe the activities of carpet salesmen and second hand car dealers," he said.
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