Experiences of SN children applying to mainstream independent schools

[Dayofpeace]

I am interested in hearing experiences of parents who have applied to independent mainstream schools for their SN children (with or without EHCPs), and been either rejected or prevented from applying.
I don't mean special schools, I mean mainstream independent fee-paying schools, in a context where the SN child is high-functioning and could easily meet the academic standards of the school, where the needs were social and emotional, and the child is not aggressive.
I have recently been through this scenario, and I'm wondering how often it happens, and in what ways it happens.
I am interested in what sort of school assessments, discussions, and rejection reasons people have experienced. Thank you!

Ours would have been accepted for year 7 entry with no EHCP and was encouraged to apply by Head. After that school was full and unlikely to have got a place.

In year 9/10 when did have EHCP rejected everywhere due to EHCP. Without EHCP I suspect they would have been offered but very few schools had places and the academic ones had many people applying for the few places and when they can pick and choose I don't think they would chose the asd kid who hasn't managed state secondary. I regret not sending mine private in y7.