I get where you're coming from OP.
I guess I'm 'middle class'. Although my parents never went to uni, my Dad was highly educated in Engineering in the forces they had high aspirations for us and both my Dsis and I both went. My dh has a degree too.
My eldest dc is now in Secondary and my youngest just about to leave Y6.
The Primary they attended was good (ish). The teachers were friendly enough (although it was the TA's that were more switched onto the pupils imo). I never totally felt like we 'fitted' in.
The parents were a mixed bag. Good, solid, hardworking parents in the main. However hardly any had any higher education and in fact most of them hadn't moved more than 2 streets away since they were children.
There were factions of parents within the school who were chaotic, uninterested and downright abusive - swearing, absent and constantly arguing.
On my first pick-up in Reception I met a Mum who was wearing a tag.
Anyway, roll on through the school and I met some lovely parents and my children did well. However when it came to choosing a Secondary School I actively looked further away from the school down the road from the Primary.
Not at all a 'bad' school, but it had no sixth form. Not a problem in itself but over the decades there has built up a culture of leaving school at 16 and getting a job. These days, many of the Leavers go onto vocational training such a beauty or plumbing.
Again, nothing wrong with that - but many of the kids I know from there don't even know about University. Unsure of what they even are. Their parents don't even consider it an option. A few parents I knew were horrified when some of their dcs said they wanted to be a photographer and travel the world (?)
So I looked for a local school that had a different vibe and a different attitude. Still a Comp, in the middle of any results tables.....but the whole attitude to educational and aspiration there is very different. There's a strong push towards the Arts too, with a heavy emphasis on drama and music. All this adds up to an atmosphere I wanted for my dcs.
My dd is about to go into Y9. She mixes with all kinds of children from affluent children with swimming pools in their country gardens to aspirational Council house pupils down the road from us. It's not really about the 'class' of pupils and parents but about the energy and importance they put into the school and the kids education.
I caused a little storm when I didn't go along with the local comp with all the other Primary School parents. They went out of their way to question me as to why. I was very tight lipped on it.
I know they thought I was a huge snob but I really don't care these days, the school I chose was right for my dc (so far anyway!).
I would go with your gut instincts.