Dictionary of oxford and cambridge, both show that word "prefect" has a capital p when it has the meaning of government official.

Should headteacher be Capitalised?

Them words are always capitalized. Looking at the examples, I would not capitalise 'teacher', but Headteacher (a specific person with a title) seems OK.

What is the rule for capitalization?

In general, you should capitalize the first word, all nouns, all verbs (even short ones, like is), all adjectives, and all proper nouns. That means you should lowercase articles, conjunctions, and prepositions—however, some style guides say to capitalize conjunctions and prepositions that are longer than five letters.