An overloaded curriculum geared towards tests and targets forces pupils to be competitive at a young age and does not allow schools to tailor lessons to individual pupils' needs, according to the National Union of Teachers and the Association of Teachers and Lecturers.
A survey of 628 teachers by the ATL found three-quarters of teachers believe the national curriculum damages the education of special needs pupils.
One primary teacher said: "I feel special needs pupils get a raw deal - sometimes they need extra time on core subjects. I also feel that the primary curriculum could be more tolerant of increasing the amount of practical work, which sometimes feels edged out by the more academic subjects."
The survey found a third of teachers said the curriculum did not meet the needs of the majority of pupils with boys and ethnic minorities also losing out.
Speaking at a fringe meeting at the Labour Party conference on Wednesday, Mary Bousted, ATL general secretary, told Mr Johnson: "The national curriculum is not working and needs a radical overhaul. If the Government genuinely believes every child matters, it is time it starts to practice what it preaches."
Her call came days after Steve Sinnott, NUT general secretary, wrote to Alan Johnson asking for an independent review of the curriculum and tests and their impact on SEN pupils.
League tables force teachers to "teach to the test" and encourage them to focus their efforts on pupils likely to reach the required standard, he said.
Earlier this month, Mr Johnson admitted government targets encouraged schools to focus on a narrow group of pupils and could work against those who had fallen behind their classmates.
Mr Sinnott also called for a new SEN strategy, including an "unequivocal commitment to the continuing need for special schools" and a review of inclusion.
Two major reports published in recent months have cast doubt on the success of the Government's policy of supporting the education of pupils with complex needs in mainstream schools.
The Costs of inclusion, commissioned by the NUT, found staff in mainstream schools were being asked to work "above and beyond the call of duty"
carrying out tasks such as changing nappies and cleaning tracheotomy tubes.
Its findings were supported by MPs on the Commons education select committee which warned the current system of statementing for children with severe needs was "not fit for purpose" and that league tables encourage schools to avoid taking pupils with special needs.
The Government is currently preparing its response to the select committee's report.