A study by think-tank the Sutton Trust found that across all children, 15 per cent of pupils who scored in the top 10 per cent nationally at age 11 in their Sats tests failed to get in the top 25 per cent at GCSE level.
However, bright boys who had been eligible for free school meals at some point in their school lives were more likely to become what the Sutton Trust terms "missing talent", with more than one in three (36 per cent) of this group underachieving at age 16.
Just under a quarter (24 per cent) of disadvantaged girls were found to underperform in their GCSEs.
The Sutton Trust has called on the government to create a national programme with ringfenced funding for highly able state school pupils.
It also wants:
- All schools to be made accountable for the progress of their most-able pupils.
- Schools that are already successfully catering for highly able pupils to be invited to consider providing extra-curricular support to expand the "horizons and aspirations of children living in the wider area".
- Schools to be encouraged to use pupil premium funding to improve the support that bright pupils from disadvantaged backgrounds receive.
The report found that areas with high levels of "missing talent" included Lambeth, Knowsley, Nottingham, Stoke, and Tower Hamlets.
Areas where highly able children from disadvantaged backgrounds went on to perform to expectations at GCSE level included Buckinghamshire, Ealing, Hackney, Slough, and Trafford.
Lee Elliot Major, chief executive of the Sutton Trust described the report's findings a "scandal", adding that they highlight a "tragic waste of talent".
"The fact that a pupils' chance of reaching their full potential is linked to their background tells us that we urgently need to do more to make sure that our most able students have the support and advice they need to thrive," he said.
"This attainment gap is holding many young people back from gaining the grades they need to get to the best universities."
A Department for Education spokesman said the government is determined to ensure that every child regardless of background is given an education that allows them to realise their potential.
"That is why our reforms place high expectations at the heart of our school system, with a rigorous new curriculum, world-class exams and a new accountability system which rewards those schools that push every child to achieve their best, rather than focusing on those at the C/D [GCSE grade] borderline," he said.
"Alongside our £2.5bn pupil premium, the result of these reforms is that the attainment gap between disadvantaged pupils and their peers is now narrowing at both primary and secondary level."