Most schools don't expect its teachers to be qualified in the subjects that they teach. I know three PE teachers, two of which also teach humanities and one who teaches science.
Academies don't require teaching qualifications at all I believe.
You're also assuming that teaching the full curriculum is necessary and desirable. It isn't; according to a head teacher I know it was based on the subjects Ken Baker thought were necessary based on his old prep school education. It baffles me as I love history, geography and RS but many children don't get anything from these subjects and their time in school could be put to better use. Parents who home-ed can allow their children the freedom to use that time to explore tech, construction, cookery, or concentrate on the stuff they really love - fiction writing, archaeology, whatever. If it wasn't for the fact I deem it necessary for my kids (none of whom have SEN) to get in the mix with people and learn the 'rules' of social interaction and friendships, they wouldn't be in school. My heart breaks when I think how much time they spent desperately unhappy in their state primary and that is the norm now due to the pressure of curriculum and testing, not the exception. Even the teachers I know think life is less pressured in secondary school, not more.