We started with State school, an only-just-good one.
Yr and y1were fine, good even.
In y2 my oldest son was diagnosed with dyslexia as well as other, related, SEN. He fell behind more and more.
We moved him, and his brother (who s more of an "average"chid who was doing well) to a private school that speialises in SEN and academic children. We knew exactly what we wanted, ie smaller classes, more SEN support and less disrution in class. It is not a "fancy" school as such, no ski trips orvextravagant extras.
It seems to be working out just fab for both f them.
However, it was only when the DC were about 8 that we knew exactly what we wanted, and what they needed. So I do not regret the 3years at State Iyswim.
You can always change your mind, it is in fact quit common to chnge at age 8/9!
So despite being a private school parent, I would say give the local school a chance