One of the main head teachers' unions has pulled out of the agreement to reduce the workload of teachers in England and Wales.
David Hart said his members were "angry"
The National Association of Head Teachers said its members did not have the money to implement the reforms.
From this Septembers, teachers are supposed to have guaranteed time off for such things as lesson preparation and planning.
Schools minister Stephen Twigg has warned heads not to break the law.
The general secretary of the heads' union, David Hart, told the BBC News website: "Our members are angry that they do not have the funding they need to implement these reforms."
He said the "stark reality" was that a significant number of schools would not be able to honour the commitment to time off this autumn.
Asked how many, Mr Hart said it might be several hundred or several thousand schools - it was difficult to say at this stage.
"I doubt very much frankly whether the chancellor's budget announcement makes any difference.
"It's all about capital money and what little he said about revenue funding wouldn't have persuaded our members that they were getting the sort of annual budget increases that they want to see."
The union has been warning for some time that not enough money was available.
Schools Minister Stephen Twigg said head teachers should not break the law by refusing to implement the government's reforms.
He told BBC Radio Four's Today programme: "I very much regret the decision that has been taken.
"But I need to make very, very clear that this does not affect what is a statutory entitlement for teachers to have planning, preparation and assessment time from this September. That will go ahead.
"And we will carry on with all the other unions that remain signed up to this agreement, with local government because it is so important for children's education that this agreement moves forward."
The government believes the changes are needed to treat primary teachers as "modern 21st century professionals" and give them the tools to raise pupil standards even further.
It says many schools are quietly introducing the changes to good effect.
The agreement was concluded between the government and all the main education unions - except the biggest.
The National Union of Teachers never signed and maintains its opposition.
Its main concern is about teaching assistant taking classes.