Hundreds of children had their national curriculum test results changed or cancelled last year following cheating or mistakes in administering the papers, a Government report shows.
Increasing numbers of cases of "maladministration" were reported to the Standards and Testing Agency (STA) following last summer's tests, according to research.
Maladministration is any act that could jeopardise the "integrity, security or confidentiality" of the tests, the report says, which covers everything from papers being incorrectly opened, children cheating, pupils being "over-aided" by those conducting the tests, or changes being made to papers by someone other than the candidate.
The report shows that, in 2012, 370 cases were reported, up from 292 in 2011 - a 26.7% rise.
There were 168 cases reported in 2010, although it is thought the figures may have been lower that year due to a boycott of national curriculum tests by around a quarter of primary schools, while in 2009 the figure was 346.
The figures cover Key Stage 2 national curriculum tests - known as Sats - in English and maths which are taken by 11-year-olds in their final year of primary school, English writing and science sample tests, and higher Level 6 papers which are also all taken by 11-year-olds, and the Government's new reading, or phonics, test for six-year-olds.
In total, 584 pupils had their results changed or annulled last year, the report says, adding that this represents less than 0.1% of pupils who took part in the Sats tests.
A breakdown of the figures shows that 399 pupils at 20 schools had their English and/or maths Sats results cancelled, 70 children at one school had their English writing sample tests annulled, 114 pupils at 39 schools had their English and/or maths Sats results amended and one child at one school had a Level 6 maths test result changed.
The rise in maladministration is partly down to an increase in the number of phonics test cases reported, the STA suggested.
It added that another cause was an increase in the number of cases of schools administering the Sats tests at an unauthorised time, which could be due to changes allowing the tests to be rescheduled up to a week after the set dates.
More than three-quarters of cases of maladministration in the Key Stage 2 Sats tests happened while the papers were being sat, the report shows.
This included 94 cases of test administrators "over-aiding" children, up from 91 in 2011 and 28 cases of children cheating, compared with 25 in 2011.
A Standards and Testing Agency spokesman said: "Results were amended at only 58 primary schools - that amounts to fewer than 0.5% of the thousands of schools where pupils took the phonics check and the Key Stage 2 tests.
"In the vast majority of cases, no action needed to be taken because it was decided the schools were not guilty of maladministration."