Norfolk announced a new round of consultation over the proposal after headteachers told The TES that they may have to sack staff.
Lisa Christensen, director of children's services, emailed a letter to heads last Friday apologising for the "distress" caused over the plans.
A TES survey showed that at least 15 other local authorities were planning to follow Norfolk and use powers that came in last year to stop hoarding.
Elaine Aylmer, head of Heartsease first school, Norwich, which is facing a pound;28,000 loss, was delighted by the fresh round of consultation.
But she said: "I fear that the damage done to the relationship between schools and the local authority will take a long time to repair. I definitely intend that my next headship post will be outside Norfolk."