John Dunford's comments came after Education Secretary Ruth Kelly said comprehensive schools had not delivered the goals of her Labour predecessors such as Tony Crosland, who served as education secretary from 1965 to 1967.
In a speech to the Fabian Society, Ms Kelly said ministers had been right to abolish most grammar schools as they were "based on the flawed science and injustice of the 11-plus". She said there would be no widespread return to selection. But the comprehensive system had limitations. There was little agreement on what a high-quality education meant, scope for schools to develop a distinct character, pupils were not put at the heart of reform and "good" middle-class and "bad" working-class schools had developed.
She added: "Comprehensive schools have done well for many, but they have not been the universal engine of social mobility and equality that Crosland hoped."
Ms Kelly said Labour's third-term vision was to shift the focus from "comprehensive schools" to one where achieving a "genuine comprehensive education" for all pupils was the objective.
Mr Dunford, general secretary of the Secondary Heads Association, said that league tables accentuated differences between schools, concentrating problems in those serving disadvantaged areas.