I'm sure they are allowed to prevent students taking a subject due to specified class sizes but iirc, they can't stop you from doing it through Open High School?
I don't know anywhere where it is stated but have had experience with students appealing to the BOS after being told by the school they can't do a subject and have had the BOS tell the school that the only way they can stop a student doing a course offered by the school is if the class is full, or if it clashes with another subject the student has chosen.
but my schools annoying, they scare you the whole year about to being able to get into the subject that you want. For example English, they said anyone with <75% overall mark wont be able to do advance, then they just choose the top 60 in the yearlies/rosa, that's so sneaky. I don't know how rollovers are going to work but if I get dropped for some idiotic reason, im making an appeal