The poorest white boys and girls are the lowest attaining group in England, save for gypsy and traveller children.
A study into how to break the cycle of white working class underachievement suggests more resources should be targeted at pupils from these families.
Currently schools get significant extra funds for a range of things, including the number of ethnic minority pupils.
The research commissioned by the National Union of Teachers and government agency the National College of School Leadership looked at how leaders worked in 10 schools where white working class pupils did significantly better than the national average for their group.
It found these head teachers did not accept social class as an excuse for failure.
As one head put it: "It's an attitude. We simply don't accept the estate as an excuse for second best; we have high expectations, every day, everybody."
Head teachers were "creative in their use of funding" but that they wanted even greater flexibility.
The report called for school funding to be "reconfigured and used sensitively" in deprived areas, in part to "recognise the impact of deprivation on the achievement of white working class pupils".
Schools are given extra cash on top of their per pupil funding, for a range of things including the number of pupils they have from ethnic minority groups and those with English as an additional language. This can amount to significant sums.
Head of education at the NUT John Bangs said: "There's a gap in terms of the support and funding streams that are available.
"It's absolutely right to support kids from ethnic minority groups but head teachers want also the flexibility to support kids from white working class backgrounds, particularly those coming from tough and deprived areas."
