no heads don't have the power
I prefer to read the legislation rather than rely on inaccurate press reports (which, in any case, refer to Wales where the law is different). Heads do have the power. For LA-controlled schools the LA won't be happy with them if they ignore directives but the LA can't sack them. Of course they may have problems if they breach any policy set by the governors. But that doesn't alter the fact that they have the power.
no one will quote you the figures for that
Read my post again. I quoted the figures for that. They are published by the government every year. Persistent absenteeism is down 40%.
education of the child is not the best way out of poverty. education of the parents is
I said education is the best way to lift children out of poverty. I didn't specify who should be educated. But schools can generally only educate the children.
the clear link between education and attainment is in relation to children who have many many weeks off ending up with lower GCSE's
Do you class 2 weeks per year as "many many weeks"? That much absence will cost the child half a grade at GCSE. If a child misses 17 days per year that will cost them a full grade at GCSE.