The heads, who had doubts about the ability of the county to fund their schools adequately, claimed to have unearthed shortfalls of up to pound;70,000 and have written to Paul Lincoln, director of learning services.
Frances Booker, head of St Clare's RC school in Clacton, said: "The financial constraints we face will greatly affect the quality of the education we can deliver."
A TES survey, with responses from more than 600 opted-out schools, revealed that the GM sector nationally was bracing itself for cuts of more than pound;100 million.
A council spokesman said: "The GM schools had notice they would receive a cut in funding. Why shoot the messenger when it is a national situation."