My child is being turned down by all the independent schools we are applying to based on his recently diagnosed dyslexia - does this contravene the disability act?

My child recently had neurodiversity screeners by a charity. They provide reports but not diagnosis and suggested his had strong signs of dyslexia and possibly ADHD. He is year 6 and due to go to year 7 in a few months time. We have applied to 3 non academically selective independent schools and they have all turned our application down. The first which is supposed to have good provision for dyslexia, turned him down on the basis of the report saying they couldn't support his type of adhd. They hadn't even met him, he doesn't have a diagnosis for ADHD and certainly there was no mention of a type. We are wondering now whether he actually has adhd or whether we were just going through a tricky developmental stage at the point of the screener. I've tried to get an ADHD private diagnosis since to rule it in or out but no providers have come back to me. I'm not happy for him to be turned down over something that is not diagnosed. We have managed to get a private dylexia diagnosis since. It confirmed his dyslexia. He scored significantly low for literacy but average in other areas and particularly high in others (98th percentile in one particular test). The conclusion was he can still be successful academically (particularly in STEM) provided his dyslexia is supported. Since then our last 2 independent school options have said they cannot support his dysexia requirements. I am told he does not qualify for an EHCP and as far as i can see the dyslexia recommendations are standard. 25% more time, pre-teaching, some small group dyslexia support and speech to text tech. All of which is supposed to be available at the last school in particular that has a specialist learning facility. Are they discriminating or can they just get away with saying they can't support him and he won't be able to keep up with his cohort?