As I see, from both sides of the table (as a teacher and parent) you can campaign for better state education- from the inside. You can become a parent governor, or a normal governor if you are illustrious enough. You can lobby your child's teacher whenever you feel their work is not up to scratch. You can pull them out if you feel you are getting nowhere.
The first is a positive way of effecting change, but ultimately takes years. The second is mostly seen as MC whinging parent syndrome- "my little Portia can do so much more than what you are giving her" is the stereotype. Second type of parent are loathed universally by schools and other parents.
What you can't do alone is change things for the better from the outside. So even if you take the plunge and send your child to the local secondary under-performing hoping to effect change the positive way, your child will spend their school career in an "improving" school. How many people are truly willing to risk their child's five years of secondary?
Most people will do whinge, complain, pull in that order. Few will become governors or volunteer at the school to see what it is truly like. I don't know very many secondaries that even welcome parent helpers.