The other thing you need for a market to work well is buyers who act rationally and have some reasonable understanding of what is going on.
How in the name of God are you going to do this in Britain ?
Look what happens when you let people make decisions about things they don't understand, like the way their bodies work. Homoeopathy, crystal healing, "angels", etc.
Pick up the newsletter that comes from your school. What % is sport, I'd give good odds that there is nothing academic at all, some will consist wholly of sport.
That's because parents like it.
The reason for the pathetically inadequate level of British education is that we have too many crap parents who don't give a toss.
Of the parents who do care a lot, many are gripped by religious hysteria.
If we look at countries where parents have a lot of input into education, we see crap. America is the best example, where education officials are directly elected and parents can have books banned from school libraries.
France, Japan and Russia which do very well have essentially zero parental influence over schools. But they also have supportive parents.