Doug McAvoy, general secretary of the National Union of Teachers, made the claim after one of his officers was elected the council's chair.
He said the appointment of Judy Moorhouse, who is the junior vice-president of the NUT, would mean the GTC would be "weaned away from the Government".
He said: "The presence of the NUT in the GTC is fully endorsed by this election. The union was successful in the election of 12 of its members to the council which has 25 members, and now has an officer of the union chairing the council. Ms Moorhouse will ensure the NUT's policies are promoted."
Ms Moorhouse, a secondary teacher with more than 30 years' experience, will succeed John Beattie when she takes up the one-year post in September.
However, Ms Moorhouse, head of year at Richmond school in north Yorkshire, said: "This is a non-political and non-union appointment. In fact, I was seconded by an NASUWT member, Sheila Mountain.
"One of the reasons I believe I was elected is because people know that when I am at the GTC, I work for the GTC alone. I shall do my very best to promote teachers' interests."
She said she hoped her year in office would see a rapid expansion of continuing professional development for teachers and a higher public profile for the GTC.
Ms Mountain said: "I seconded her because I believe her to be the best person for the job. She has excellent chairing skills and is a practising teacher. Although everyone thought at first that there would be union rivalry, this has not materialised and members have set these aside for the good of the council."
Carol Adams, the GTC's chief executive, also said the GTC operated beyond union affiliations. "Judy Moorhouse has been a leading member of the GTC for the past four years and her appointment is an extremely positive step," she said.
Mary Bousted, general secretary of the Association of Teachers and Lecturers, said Mr McAvoy's statement was outrageous. "The GTC exists to represent all teachers," she said. "Perhaps the NUT feels so far out of the loop it needs to claim it has influence in other ways."