Fewer teenagers scored at least five Cs at GCSE this year - the first time the numbers have dropped in almost a decade.
Official figures show that 58.6% of pupils in England gained five A*-C grades, including English and maths, this year - down almost half a percent on 2011.
Statisticians said the drop was down to fewer English entries from private schools.
But concerns were also raised that the fall was linked to problems with the grading of GCSE English.
Overall, there was a 0.4 percentage point drop in the numbers of pupils achieving five A*-C grades, including the two core subjects, down from 59% in 2011.
It is the first fall since 2004/05, when the Government changed the way it collects the figures.
Government officials said there has been an increase in overseas students attending UK fee-paying schools, and many of these either do not take English, or take English as a second language, which is a different subject, and this accounts for the drop.
Russell Hobby, general secretary of the National Association of Head Teachers, said that this year's GCSE results had been overshadowed by the GCSE English "shambles".
Headteachers have claimed that thousands of students received lower than expected results in GCSE English in the summer after grade boundaries were raised between the January and June exam sessions.
Mr Hobby said: "This year, unfortunately, GCSE achievements have been overshadowed by the shambles surrounding English.
"Having seen grade boundaries moved between January and June, and papers regraded in Wales but not England or Northern Ireland, it is our feeling that the drop in the number of students getting five A*-C grades including English and mathematics is related to this.
"We can see from the data that schools are continuing to make excellent progress but, nevertheless, thousands of young people have had their results and their futures hampered by the GCSE marking fiasco.
"We continue to prepare the framework for a legal challenge to see these wrongs righted, with the aim of English being regraded, and we are optimistic in wanting to see official data which will reflect this regrade in the near future."
The figures show that in state secondary schools alone, there has been a 0.1 percentage point rise in the number of pupils getting five good GCSEs.
In total, 58.3% of state school pupils achieved at least five Cs, including English and maths.
More than four in five pupils (82.5%) from all schools in England gained five or more GCSEs at grades A*-C in any subjects, up two percentage points on 2011.
The statistics also show that rising numbers of pupils are being entered for and achieving the Government's new English Baccalaureate.
To gain the EBacc pupils must score at least a C grade in English, maths, science, history or geography and a foreign language.
This year, one in four pupils from all schools in England were entered for all the EBacc subjects, with 18.1% achieving the award.
This is up on 2011, when 23.8% entered and 17.6% achieved it.
A Department for Education spokesman said: "It is welcome that more students are studying the core academic subjects that will open more doors to them for their future.
"The EBacc is the platform for young people to go on to A-levels and high-quality vocational study, and is helping us compete with leading nations who expect all students to study a rigorous academic core."
Verity O'Keefe, employment and skills adviser at EEF, the manufacturers' organisation, said: "Today's drop in the number of young people achieving five good GCSE passes, including English and maths, shows that we are still some way off the mark the economy needs to grow the pipeline of people with good basic skills.
"Many employers use similar benchmarks when recruiting young people, with three-quarters of manufacturers prioritising attainment in maths, English and the sciences when recruiting apprentices.
"However, a lack of attainment in key subjects is still restricting firms' ability to fill vacancies and government must now set a target of 65% of students achieving five good passes which includes English and maths."