I think that the education of the parents has a more significant outcome on a child's attainment than income. (Especially as many working poor don't have much more money than those on benefits.)
I feel that children who live in households where no adult has five GCSEs or equivalent should get extra support at school. Often these families aren't entitled to benefits because the parents do work so currently don't get the pupil premium.
It is harder for uneducated parents to support their children with homework than someone with a degree. Better eduated mothers are better at getting their children's needs met as they are often more articulate. For example making sure that statemented child gets what they are legally entitled to. (Getting a child assesed by an ed pych so that the child's dyslexia is spotted.)
Unskilled people often do physically hard work for very long hours for very little money. I believe that a child with unskilled working parents is at a major disadvantage as their parents are time poor as well as cash poor.