The proposal was part of the move to include value-added scores in the primary performance tables.
Value-added scores rate schools on the progress pupils make between ages seven and 11, and have been welcomed by unions as fairer than raw scores.
But there were widespread concerns among the 495 schools piloting the scheme that an A to E grade could be misinterpreted as rating the overall quality of the school rather than the test results.
In the pilot scheme, Pooltown junior in Ellesmere Port, Cheshire, was rated D. Amanda Whitley, Pooltown's head, said: "In a school like ours where staff work exceptionally hard to get results, we are constantly being knocked back and told we are not good enough."
Pooltown has a high proportion of children claiming free school meals and pupils arrive at seven with lower than average test scores.
Last year 56 per cent of its Year 6 pupils gained the expected level 4 in English and 63 per cent in maths. Almost a quarter of the children had special needs.
Joan Potts, head of neighbouring Atherton nursery and infants, said: "We are looking at different ways of recording pupil progress and progress in smaller steps. The present system does not allow that progress to count."
Professor Peter Tymms, of Durham University, issued a warning last year that the value-added scores were too simplistic. He said social factors which led to low test results could also lead to lower than average progress. Comparing progress in schools in disadvantaged areas with average national progress could mean such schools remain bottom of the tables.
The Government is now consulting on proposals to drop the A to E bands but keep a value-added score as part of the consultations on the primary league tables.