If I want to leave my job by the end of this half term, when do I have to get my resignation in?
Check your contract. It probably states that you need to give two months'
notice, except at the end of the summer term when you need to give three months. This means you are too late to resign officially for the October half term. However, if your replacement is available, it may be that your head teacher would be willing to accept a shorter period of notice.
However, heads are not obliged to let you leave before the end of your notice. If you quit anyway before you should, do not be surprised if you don't receive a glowing reference.