This is actually a myth btw. I've posted the evidence on the forum before; in almost every study ever conducted on the issue, the "quality" of school that you go to has almost no effect at all on your life chances.
Sending kids from the ghetto to a private school and sending rich kids to an underfunded public high school produced no differentiation from the norm of academic achievement. Much more important is the social class that you come from. Rich kids will be schooled well no matter where they go and poor kids will always be fucked.
Social mobility is about social class differences rather than educational standards. Creating a larger middle class, for example, seems to be the best way to do that and the best way to achieve a large middle class is to invest in underfunded public services in working class areas. Addiction, adult care services, Children and Young People's Services, etc.
Essentially, if your Mum is a crackhead and your Dad is a drunk then it doesn't matter if you go Manchester Grammar or Moston Brook, you're pretty much going to have a shit life.