The remaining 6,100 or so children were turned away because they did not meet other entry criteria as closely as those who were offered places, such as the distance they live from the school.
A small number of pupils who applied for and sat more than one test will be included in the figures.
They do not include children who have narrowly missed a place at "superselective" schools, which only take the top performers and do not have a pass mark.
If a similar number of eligible pupils are being rejected from the other 108 grammars in the country, it would mean that nearly 20 more establishments would be needed to meet the demand for places from about 15,000 extra students.
Bob McCartney, the chairman of the Grammar Schools Association, said: "These statistics demonstrate the great demand for grammar schools compared to the small number of places available and the unfairness to children who are qualified to fill them but are denied a place.
"The Government continues to blatantly ignore parental choice. Its approach is based on political motivation and not the pursuit of education excellence."
New Government admissions rules introduced last month make it easier for oversubscribed schools to expand or even establish "overflow" or "satellite" schools nearby.
However, there is no new capital funding for buildings and it is unclear whether a "satellite" grammar school would contravene the 1998 legal ban against the setting up of new selective schools.
Wallington High School for Girls, in Sutton, received 1,400 applications for 180 places and had to turn away more than 300 pupils who passed the 11 plus.
Barbara Greatorex, the head teacher, said: "I just think it is a shame that the opportunities that grammar schools afford are not more widespread. Most grammar schools are so oversubscribed that they take as many pupils as they possibly can but without capital funding, they do not have the space to take more."
But the admission rule changes have offered renewed hope in some areas which do not have grammar schools or have an acute shortage of places, such as Sevenoaks in Kent.
Plan are under discussion for existing grammar schools in Tonbridge and Tonbridge Wells to establish campuses for the 1,100 Sevenoaks children who travel about nine miles everyday to grammar schools in other towns.
Michael Fallon, the Sevenoaks MP, said: "The cost and time spent transporting these children is a huge waste and there is growing demand for grammar school places beyond that, including a big new housing development in north Sevenoaks.
"Parents, primary schools, head teachers are increasingly vocal about the need and the county council is supportive.
"We are actively exploring the establishment of a campus of two existing grammars and there is definite interest."
A Department for Education spokesman said: "We're giving all schools the freedom to offer more places but they will not be getting money from the department to expand."
Ministers are instead funding new free schools. An extra ￡600 million to build 100 more free schools will be announced in Tuesday's autumn statement.
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