Well I've only glossed over the responses here.
So... in response to your initial question, No, I dont thing YABU to consider moving to get your children into 'better' schools. Even if it means downsizing.
That was the basic question wasnt it - regardless of who considers what to be a 'better' school?
We are considering moving ourselves for this very reason (not yet, DS is only 2) - we won't be able to afford private but there are some grammar schools that DH has his eye on and at this time, they look very appealling for many reasons. I actually would be quite happy to send DS to one of our local schools based on what I've heard BUT if we can give him 'better' opportunities/education by moving elsewhere (and I'm not talking a big shift from where we are now) then I will. IF it possible when the time arises. And dependant on his own emerging abilities as well - those factors are unknowns at the moment.
Obviously as people have stated, it depends on how you qualify those 'better opportunities' - by Ofsted report, results, word of mouth, personal 'inspection' etc etc.
In my own experience, I know for a fact that I got a 'better' education from my private school - this is compared purely to the specific school my step-sisters attended. We had fantastic facilites in lots of areas, and lots of encouragement/motivation.
But, I'm not naive enough to think that just because my education was good compared to theirs, this is the case for all independant schools. As people have said each school will have its own merits and downfalls, and that needs to be explored properly without the assumption that they wont be any good, or conversley, will be 'good'.
So just do your homework and base it on that. You clearly want what you think is the best for them and it doesnt matter if other people think you're a snob, or even if you are a snob. I dont give a rats ar*e what you decide, but if it means losing a house you love in an area you love then you NEED to investigate and not make assumptions. Good luck.