He said Government reforms had caused havoc and disillusionment and he warned: "The political moves to dismantle comprehensive education by encouraging selection are now likely to recreate the infamous sink-schools."
Mr Varnava, who was head of Norwood school in south London for more than 13 years, is now an advisory head with the borough of Lambeth. The 59-year-old had to quit his job as headteacher to become NAHT president.
He urged the Harrogate conference to regain control of education and said: "We are directed by a collection of instruments of government whose inherent disharmony prevents the very stability and coherence we aim for.
"Persistent pressure is helping to change what directly concerns us: the practical implications of reform. We are slowly and surely succeeding by dissent, not disobedience. As initially prescribed, the national curriculum and testing and inspection just would not work, any more than the poll tax did. And as for compulsory worship, even church leaders state that worship cannot be enforced."
He attacked Government claims of increased education funding and said the last thing children needed was a league table. "Every school is unique. It is meaningless to compare schools with different populations and objectives, in different locations, with different levels of financial, material and human resources."
NAHT national council member Liz Paver said primary schools were having to work with children who had no respect for themselves or the adults around them. "These children cannot play or co-operate. They swear at each other and kick each other. The only thing they know is violent action."
David Hart, general secretary of the NAHT, took up the theme of parental responsibility. He said permanent exclusions were due to rocket to 10,000 a year, a three-fold increase in three years. "No teacher should be expected to deal with violent or disruptive behaviour with one hand tied behind their back," he said.
Mr Hart said: "There has been a deafening silence on how the Government intends to ensure that all parents discharge their responsibility for contributing to their children's education, and for their children's behaviour." If the Government was serious about raising standards then it must pay heads and deputies a decent salary. He said there was evidence of increasing difficulties in recruiting heads in England and Wales because of low pay and long hours.