I can see you've already made your mind up really, but just in case this helps:
I was in the same situation as you before my dd1 was due to start school. My parents offered to fund her place at a private school if we wanted it. I looked at the local (highly regarded) private school and I didn't warm to the people I met there. I listened to the privileged little girls bitching about each other and it turned my stomach. I didn't want my dd to be bitched about by them, or worse, turn out like them.
So I sent her to an absolutely excellent state primary. It is 'outstanding' according to OFSTED and I agree. The other children in her class are lovely, and the school is great pastorally and educationally. She's reading brilliantly now at the end of reception and there is none of the nonsense I've seen in previous posts about keeping advanced readers back because of a policy of working through all the stages. They are happy to let her work at her own pace and they seem to differentiate the work well for the mixed ability class.
I'm stating the very very obvious, but it really is all about what the particular schools are like. I can see that you love the private school, so presumably that would be the right choice for you. But I don't think you should accept the blanket notion that private schools are 'first class' while state is 'economy'.
Also, if your dd should turn out to have any special needs, you would find a state school much more useful as the school would work with the NHS speech therapist / occupational therapist / physiotherapist / education psychologist or whatever. Whereas if you go private you would have to fund all that stuff yourself. May not be relevant but just a thought.