A mean-spirited cheque
You are paid from the start of your contract. This looks like a device to save money for the school, and is mean-spirited. Whether this is illegal will depend on whether you are treated differently from other teachers. I can't image that anyone who changed schools within the same authority would accept a break in service and the loss of four days' pay, even though they would be paid by a different school. If it does not apply to them, why should it to you since, as you point out, you were available for service from January 1? Contact your professional association and find out whether this is common practice in your authority.