The number of appeals over national curriculum test results for 11 and 14-year-old pupils is expected to soar this year, amid concerns that marking has been rushed to deal with a massive backlog of unmarked scripts.

The National Assessment Agency has agreed to push back the deadline for appeals until September 10 – or ten days after the start of the autumn term – to deal with an avalanche of expected appeals.

This will mean that final marks for many papers are unlikely to be delivered until well into the autumn term, causing difficulties for pupils who are trying to make decisions about which GCSEs to study in the next academic year.

The latest marking figures show that more than a quarter of 14-year-old pupils will not get their Key Stage 3 results before the end of term.

According to ETS, the private contractor at the centre of the marking debacle, 29 per cent of English results were still not ready for publication yesterday.

Seven per cent of Key Stage 3 maths results and 9 per cent of science results were also not ready, according to ETS, which is in the first year of a five-year, £156 million contract to mark the key stage tests.

Although the delay in publishing the results will be hugely frustrating for hundreds of thousands of pupils who worked hard for the tests, John Dunford, general secretary of the Association of School and College Leaders, said that schools and parents would be more concerned about the possible lack of accuracy.

“The Government and Ofsted use the SATs results to make judgments about whether schools will fail their inspections, and heads can lose their jobs as a result,” he said.

“Results will be scrutinised this year as never before, and the number of appeals is almost certain to rocket.

“Every year there are complaints about the marking of the Key Stage 3 tests, especially in English. It looks likely that the situation will be even worse this year.”

Martin Ward, deputy general secretary of the Association of School and College Leaders (ASCL), said that he had received calls from a number of secondary heads yesterday who had complained that the results their pupils received bore no resemblance to teachers’ expectations.

The Guardian reported last night that Kathleen Tattersall, the head of Ofqual, the regulator of qualifications, exams and tests in England, had called for all of this year’s SATs results to be annulled if the quality of marking turns out to be as bad as is now feared.

ASCL is calling for the entire Key Stage 3 testing system to be reviewed. Mr Dunford said: “When the present furore has died down, it will be important for the Government to take a long, cool look at the testing system that has been created over the past 20 years. As I have said for many years, it desperately needs changing.”

The problems are not limited to secondary schools. On Monday, Ken Boston, chief executive of the Qualifications and Curriculum Authority, the body responsible for overseeing the national curriculum tests, assured MPs that marking for the Key Stage 2 primary school tests was “100 per cent complete in all subjects”.

Mick Brookes, general secretary of the National Association of Head Teachers, said last night that he was still receiving reports from primary school head teachers who had not received results. Ed Balls, the Schools Secretary, has ordered an inquiry into the marking shambles, which will be chaired by Lord Sutherland of Houndwood.

Michael Gove, the Shadow Schools Secretary, said that confidence in the Government's handling of the testing system was collapsing. “We must have an interim report from Lord Sutherland within days so that we can ensure next year’s tests aren’t mired in similar chaos,” he said.

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