The National Association of Head Teachers has reported a 30 per cent increase on this time last year in the number of requests for help from heads facing accusations of irregularities over tests for 11-year-olds this summer.
Of the 60 calls about national curriculum tests received by the union over the past month, about 25 involve serious complaints alleging maladministration.
At least seven cases of cheating have so far been investigated this summer by the exam watchdog, the Qualifications and Curriculum Authority.
In four schools - Hanover in Islington; Merstham in Surrey; Peel Brow in Bury, and Wyndham in Newcastle - results have been voided because papers have been altered or children given help.
David Hart, NAHT general secretary, said: "The atmosphere surrounding league tables and targets has reached such a pitch that people are willing to allege tampering, even when schools are innocent.
"There is intense pressure on heads of successful schools as well as schools in difficulties. Performance management and performance-related pay is adding to the pressure."
A large proportion of complaints come from parents, according to the NAHT. Some are concerned that children with special needs, who perform better in tests than predicted, will lose support at secondary.
Mr Hart said: "It is quite clear that any attempt to look at papers before children sit them is unwise.
"And an invigilator who prefers to walk about the class during a test rather than sit in front of it can be vulnerable to complaints that they were assisting."
Ministers will be grilled about the growing and "unhealthy" pressure on heads when they appear before the new education select committee in the autumn.
The QCA refused to reveal how many cases were being investigated. Last year 147 schools were reported for cheating or failing to follow the rules. In 10 per cent of cases investigated, there was an adjustment to the final marks. In two cases, the results of whole schools were annulled.
SEVEN SCHOOLS INVESTIGATED
THE following schools are among those being under investigation by the QCA:
* Kirkby and Great Broughton primary, Northallerton. Head David Scott suspended. Allegations of irregularities in national maths tests.
* Peel Brow primary, Bury. Head Mike Duce was suspended and now on sick leave. Mental maths results declared void.
* Boothstown Methodist School, Salford. Head Jane Otway suspended then reinstated and results stood. She faced a disciplinary hearing over exam procedure. Deputy head Julie Dove, suspended, now off on long-term sick leave.
* Heybrook primary, Rochdale. Head Rod Weatherall cleared of any wrongdoing.
* Hanover primary, Islington. Head Cynthia Thumwood facing suspension but on sick leave. Allegations that answers were changed before scripts sent.
* Wyndham primary, Newcastle. Head Helen Quick resigned after admitting altering papers.
* Merstham primary, Redhill, Surrey. Results cancelled amid allegations that staff helped pupils to answer questions. Head Jill Vereycken went on long-term sick leave a week after the key stage 2 tests were sat.