The figures are revealed in a document from the National Assessment Agency (NAA), which is overseeing a marking process widely condemned as shambolic.

Last year, markers sent a sample of 10 scripts to a supervisor, who checked their work. In key stage 3 maths, they were allowed to continue marking if the scores they awarded to pupils varied from those of their supervisor by up to 20 out of 1,500, or 1.3 per cent.

This year, markers completed an exercise at the computer screen, when they were faced with six theoretical scripts to check their suitability to start marking. Under this system, they were allowed to be out by 90 marks from a total of 900, or 10 per cent, the agency’s document shows.

Differences across other subjects ranged from nearly twice as many errors allowed in KS2 science this year compared with 2007, to more than six times in KS2 reading.

A supervising marker for KS3 maths said: “The number of errors being allowed is enormous.”

A NAA spokesman said direct comparisons between the two years were impossible because the system had changed. This year, pre-checks aimed to root out the very worst performers. Further checks after markers had started were carried out and, at this stage, the number of errors allowed in 2008 was more in line with those in 2007.

Ministers have said they have had no part in the decision to appoint ETS Europe as contractor for test marking. However, minutes at the Qualifications and Curriculum Authority from 2006 record that Department for Education and Skills officials were involved in the procurement process which led to the contractor being appointed.

The Government is to investigate the extent to which teaching in English schools is distorted by the testing system, a minister said this week. Jim Knight, the schools ministers, told MPs that the Government would shortly publish a statement of its intention to “bottom out the evidence” on the extent of teaching to the test.