A new champion for gifted and talented children is urging schools to identify England's brightest one million pupils.
The government spends around £13m on gifted and talented support
Former head of the literacy strategy John Stannard will challenge the 300 secondary schools that do not identify their gifted pupils to do so.
Schools Minister Andrew Adonis said more able state school pupils must be helped to reach their full potential.
Some 91% of secondary and 65% of primary schools identify their gifted students, 733,000 of them in total.
But this week Gordon Brown announced he was expanding the gifted and talented programme, which enables bright pupils to benefit from after-school, weekend and summer events, to assist one million pupils.
He also announced an inquiry to report on how applications to universities from pupils in comprehensive schools in disadvantaged areas could be boosted.
Lord Adonis said schools needed to recognise when a child needed extra help to develop particular abilities and talents they might have.
He added: "At present, young people from higher social groups are more than twice as likely to go on to university than young people from lower social groups.
"This gap needs to be narrowed dramatically if we are to make the most of the nation's talent.
"It is simply not acceptable for a secondary school to be refusing to identify very able students who need extra support to fulfil their talents."
Teachers are expected to use assessments and special tests to discover which children are their brightest, as well as the result of "key stage" tests at seven, 11 and 14.
Schools are urged to identify their talented pupils on a termly basis through the school census.
Ministers have said they want secondary school teachers to identify pupils who meet the published standards for the top 5% nationally.
But they are also encouraged to identify other pupils who might be gifted and talented - this has typically meant the top 10%.
Primary schools are asked to single out pupils they judge to be gifted in relation to their year group.
In May, the government said the programme offering extra summer study to gifted and talented children was being extended.
A new network of university-led summer schools was due to provide day and residential courses for an extra 22,000 very able children from this summer.
Universities such as Cambridge, Durham, Bristol and York are working with schools to stretch the brightest pupils.