In general, mainstream private schools are very good at supporting children with what I would call minor SEN, on the dyslexic or dyspraxic spectrum, high performing ASN or mostly controlled ADHD. They have zero desire to take on disruptive pupils, regardless of the cause for the disruptiveness.
The above is often why parents choose them.
It is hard to defend inclusive SEN teaching in the state sector and choose a private school which doesn’t have to worry about it.
At one of the schools I used to teach at, there were about 100 (out of 600 odd) on the SEN list, but the majority of them had no formal diagnosis and a fair few were, in (polite) old fashioned terminology, just not academic. The ‘Head of academic mentoring’ (this is new popular private school term for SEN person) was constantly battling with parents to keep the list down to a size that actually made it possible to help those with genuine need (if you teach a class of 24 and 10 claim SEN, it is impossible to remember who they are or help them).