Members on the left of the executive are angry they were not informed that the union was negotiating with Oxfordshire County Council to become a partner in a zone. The news was announced by Mr McAvoy at an action zone conference last week.
He argued that the move would protect the interests of Oxford members who had already given their backing. He said the NUT could join other zones if local authorities accepted its ground rules - including protection of pay and conditions, no profits for business partners and union representation on zone forums.
Mr McAvoy, due for re-election later this year, said the NUT would also shore up the role of councils in leading zones as that role came under threat. But he was criticised by his challenger for the post of general secretary, Christine Blower, who said he had unilaterally changed union policy.
"To become a partner in a zone puts the union in the position of representing the employers rather than the employees. That's a tension with which it would be extremely difficult to live," she said.
The bid, for a part of Oxford including the troubled Blackbird Leys estate, is well-advanced and backed by a charitable trust which will provide the private finance.