Have only read the OP so apologies if repeating something else someone else has said, or for jumping just in time to be slagged off
I also had a problem when deciding between a private school that seemed excellent and a very good state one. If money is not a problem, the walkable one issue will sell it to me (I drive for more than half an hour each way to take DS to school), being able to participate in the community that is meeting around your house is another inmense bonus, as it involves plenty of play dates and helping each other out to collect children, drop children, some new friends in the area for your, etc.
Regarding the "nasty" clique at the doors of the private one... I agonised about this. I attended a private school and being the daughter of one of the teachers, a rather "alternative" type one, I really had a bad time so I was fearing the story will repeat again when at the doors. The thing was that, I had the oportunity to go to parents evenings at both schools and soon realised that I had more in common with the parents of the private school than with the ones in the other one. (Don't take me wrong here, the ones in the other school were also fantastic people, but as a expat I felt somewhat isolated and very noticeable, and I found this private school full of mums that were exactly in the same circumstances as I was. So we had some common ground for friendships to flourish, therefore it wasn't long before I was leading the one and only "clique" at the doors .
It is not a mean clique, we started having coffee after droping off the children on wednesdays and so many people started to join us that now we are more than 15, everybody is welcomed, even those nasty alpha mums who refused to say hello in the early days ).
BTW I'm not a yummy mummy, far from it, I'm not rich, I have travelled a lot though but not in luxury IYWIM, but I feel this other women at school may be richer, prettier or whatever but I don't care because I like them for what they are inside and I supose that's why they like me too