My contract says I have to give three months' notice in summer term and two months' in other terms. No date is mentioned. So if I wished to hand in my notice on August 1 and leave on November 1, I would be legally entitled to.
It would be unpopular but not a breach of contract, I think. It follows that the head who wrote to you has no choice but to accept the resignation.
The option Archimedes gives of "rigidly enforcing the contract" making the teacher serve another term at the school is wrong. They would only have to serve a few extra days.
Archimedes replies: Not everyone's contract is identically worded. If the teacher was employed under the terms of the Burgundy Book, which specifies resignation dates, then those terms would apply.