Schools minister Lord Adonis last week called for independent schools to sponsor or co-sponsor academies or become academies themselves, no longer charging entrance fees.
They would be exempt from the £2m sponsorship requirement that other organisations have to pay when they set up academies.
But Nansi Ellis, acting head of education and policy at the Association of Teachers and Lecturers, said the proposals did not answer concerns about accountability, admissions, or the working conditions for teachers and support staff in academies.
Steve Sinnott, general secretary of the National Union of Teachers, branded the move "extraordinary" and said it showed current sponsors lacked the educational expertise that is needed to run schools. "If the current sponsors are not contributing anything educationally to academies why not remove them?" he said.