Relations between pro-agreement unions and the National Union of Teachers are close to breaking point over the NUT's vocal opposition to the deal.
Unison, the support staff union, and the National Association of Schoolmasters Union of Women Teachers have written to the NUT expressing their anger at the union's threat to boycott the work of assistants taking classes.
Eamonn O'Kane, NASUWT general secretary, said: "If the NUT is getting involved so that it can frustrate the agreement, then there will be a real problem."
Brendan Barber, general secretary elect of the Trade Unions Congress, has so far failed to broker a peace deal between the unions.
The Association of Teachers and Lecturers is also reconsidering its relationship with the NUT following an advert placed in last week's TES attacking the agreement.
John Bangs, NUT head of education, said that if other unions tried to exclude his own from local workload talks they would be overturning a decision that had already been taken by the employers.
Graham Lane, Local Government Association chair of education, said: "We want to talk to all recognised unions particularly as in some areas the NUT is the majority teaching union."