A follow-up survey by the education watchdog, published on Tuesday, said standards of primary training had improved markedly since the first inspection round was completed in 1996. It had revealed "varied standards and some frequent failings".
The new study found that all 72 providers of primary training in England were now providing at least adequate courses in numeracy teaching, while only 4 per cent of courses in literacy teaching were poor.
The survey was ordered in 1996 by chief inspector Chris Woodhead, who felt the first inspections had painted too rosy a picture. Training institutions protested vigorously but unsuccessfully against the re-inspection, which concentrated on literacy and numeracy. Four institutions were failed but all passed a third inspection.
David Taylor, head of teacher education and training at OFSTED, said the standards now required of trainees were "rigorous and demanding", but there was no room for complacency.
"A minority of trainees still exhibit an unacceptable degree of uncertainty in their own subject knowledge and understanding. And not all courses are yet equally rigorous in what they expect of their trainees when assessing them for Qualified Teacher Status," he said.
The report said: "Most courses now recognise the importance of phonics in the teaching of reading and include some training on phonics as a decoding strategy." However, trainees were often not shown how to plan a structured programme of phonics teaching over a period of time.
In number, providers were generally showing trainees how to teach accurate, rapid mental calculation and efficient methods of computation.
But the quality of trainees' monitoring, assessment and recording of pupils' numeracy and literacy skills was still an important area of weakness. Improvements were also needed in information technology training, where trainees often had "very limited opportunity in schools to observe information communication technology being used well or to use it themselves in teaching".
The Universities Council for the Education of Teachers welcomed the report. Its chairman, Mike Newby, called on OFSTED to end the continual cycle of intensive inspections - currently held every two years. "The constant procession of inspectors has become counter-productive," he said.