Whizz I haven't read the whole thread, but this is my view, which is based on dd in y1 at local infant school, and ds, who is in reception at private school.
At this age, I can barely distinguish the difference in fee paying and not, in terms of the quality of teaching. Both schools my dcs are at are very good, but really, if I'm honest, there's not a huge amount in it. Where ds' school adds value, is, in the small class sizes, the 650 acres of run around space, and the different things he tries. DD will eventually go there when she leaves infants, but honestly, there's not much in it at this age.
What worries me about dd being in a class size of 31, is that as an averagely good, hitting all the marks, compliant child, she gets a bit left out, as she is neither extremely bright or naughty. For me - this is the main thing with a smaller fee-paying school, but this clearly isn't the same for everyone, as every child is different.