What year is he in? What reading scheme does the school use, and what level is he on within that scheme? Which stage of phonics are they learning in class at the moment?
You mention a 'constant battle' with the school with regard to reading - that's not good! It sounds like it would be a good idea to have a proper conversation with the teacher / literacy lead, to understand the rationale for their approach.
It would be helpful to know whether they are trying to keep him reading books that only use the phonics he has officially learned in class. If that's the case, and they are stubborn about it, you you might have to just roll your eyes, put up with one simple book per week, and supplement yourself. (Other posters have made good suggestions about accessing free/cheaper books.)
Fortunately, my DD's school were quite flexible, and let her go up the reading scheme and onto free reader very quickly. She still engaged with the phonics lessons though - they formalised some of the rules she'd already worked out for herself, and consolidated her understanding. (I don't think the school's flexible approach was good for all the kids - it was a bit 'mixed methods' and old-fashioned, and they hadn't invested in a single book scheme, and I'm sure it did some of the children no favours!)
Ask when they last assessed his reading. Did he skim read, guess, struggle to decode trickier words? Were his comprehension and inference skills up to the level that they'd expect from that level of book? Did he put expression into his reading?
With keen readers it is so easy for them to get a bit careless in their desire to get to the next stage of the book. My DD went through a phase of occasionally adding or missing a word, which sometimes changed the meaning of the sentence, or guessing a word from its general shape. Her storytelling was great - full of expression, with different 'voices' for characters - but the accuracy wasn't 100%. I had to go carefully so as not to upset her, but just asking her to read that word or sentence again would reveal the mistake, and quite quickly she learned to be careful, and to realise why it was important.
We would also talk about what individual words actually meant, and try to come up with words that mean something similar, and then explain the slight differences and why you'd use on rather than the other. She has a pencil and paper by her bed, to jot down new words or a page number if there's a longer reference that needs discussing, and she has an electronic dictionary bookmark as well.
Comprehension and inference skills come more gradually. Ask him to guess what might come next, imagine how a character might be feeling, ask him to explain what it is in the text that makes him think they feel that way.
Sorry, that was long! Best of luck with speaking to the teacher.