The regulator insisted it would be inappropriate for either set of exams to be regraded.
It called for June's papers to be regraded in line with the January C-grade boundaries.
The education secretary should have taken the lead from Wales and regraded this year's English GCSEs.
The NUT said "the injustice" should be "put right" by exams being regraded, not re-marked.
It led to the exams of around 2, 300 Welsh pupils being regraded by the WJEC exam board.
The regulator insisted it would be inappropriate for either of the sets of exams to be regraded.
It came during the intense negotiations in early September over how and whether the grades should be regraded.
In Wales, exam papers were regraded, but the dispute has continued in England.
It has served court papers on exam boards AQA and Edexcel, detailing the case for the exams to be regraded.
More than 38, 000 exam entries in England, Wales and Northern Ireland were regraded after schools asked for re-marks, the exams watchdog Ofqual says.
An alliance of heads and teachers' unions is continuing to press for June's papers to be regraded in line with the January C-grade boundaries.
Mr Andrews is demanding that papers in Wales are regraded, she says, because pupils in Wales can't be seen to be failing to improve.
Heads want to have the disputed exam papers regraded - and have rejected the offer that pupils should be able to retake the exam in November.
Mr Andrews ordered that papers be regraded and he has since set a new Wales-only grading system for the subject to avoid a repeat of the row.
In October an alliance of head teachers and councils launched legal action against Ofqual and two exam boards detailing the case for the exams to be regraded.
BBC: Heads challenge Ofqual to publish all GCSE grade research
Lawyers representing the alliance of pupils, heads and councils argued for the June exams to be regraded in line with exams taken in January when the boundaries were lower.
The regulator insisted it would be inappropriate for either of the sets of exams to be regraded and students would be given an extra chance to resit the GCSE in November.
Some 2, 300 students who took exams set by the Welsh exam board WJEC in Wales have already been regraded on the orders of the Welsh government, which regulates exams set there.
Lawyers for the alliance have claimed thousands of students missed out on the grades they needed because of a last-minute "statistical fix" and have argued for the June exams to be regraded in line with those taken in January when the boundaries were lower.
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