Schools like that Bradford one are not available to all because schools like that select their pupils in order to keep out those who are
a)academically inferior
b)socially unacceptable.
Parents do the same - those who want their children to have the best education possible will seek out the best academic schools even though the school on their door step is more than able to deliver the education they seek plus there are a lot of parents who only want their off-spring mixing with their idea of the socially advantageous and acceptable sort.
It is too simplistic to blame the government. The question that should be asked is what support mechanism is there available to ensure that poor kids from deprived backgrounds, who are bright and who want to learn but find that the only schools available to them are the "sink" schools, have the opportunities afforded by the successful schools available to them.
Like it or not, schools reflect thir intake and schools in socially advantageous areas will tend to do much better than those in socially deprived areas. Kids from socially deprived areas are the ones who have very little choice about the type of school they attend.
As for Alex, I'm delighted for him. As for his mother, I hope she will use this time to get a better job and not keep relying on others to pay her way.