But unlike in Wales, where Sats are no longer compulsory at key stage 2 and will become optional for 14-year-olds next year, teacher assessment in England would continue to be supplemented by testing.
In his boldest comments on testing since becoming head of the Qualifications and Curriculum Authority in 2002, Ken Boston said: "A good amount of the testing currently done at seven, 11 and 14 could be marked by teachers."
Under a new system, which Dr Boston said could be introduced over 10 years, pupils would no longer sit externally-marked tests in May. Instead, teachers would select tests to give pupils when they chose from a "bank" of assessments similar to current tests.
They would mark the tests themselves, with a sample of perhaps 30 per cent sent away to be moderated by external examiners.
Speaking at a conference to launch the QCA's first annual report, Dr Boston said that there was need for caution over any changes. Some external assessment could be retained, initially, for the KS3 tests. But scrapping the bulk of external key stage assessment would have several advantages, including reducing the need to find thousands of markers every year.
Schools could also time the tests to dovetail with pupils' learning programmes. They could get the results sooner than at present, and then use them to respond to pupils' learning needs.
The new testing system would still be compatible with league tables, he said. All seven, 11, and 14-year-olds would continue to be tested. Their results would be aggregated to give results for each school as well as statistics for the whole of England.
However, Dr Boston's call is unlikely to be taken up by the Westminster government. Ministers are placing more emphasis on teacher assessment at KS1 from this year. But they have resisted all calls to do so at KS2 and 3.
In Wales, more than half of primary schools have requested external marking for this summer's voluntary KS2 tests. Sats are being phased out and a new key skills test for 10-year-olds, designed to aid transition to secondary school, is being developed.
KS3 tests are compulsory this summer but optional next year. At both key stages, teacher assessments will be subject to moderation arrangements to keep standards consistent. Wales has never published primary performance tables and has abolished secondary tables and KS1 tests.
Dr Boston also re-ignited the debate on the future of A-levels. The Tomlinson review proposed getting rid of the "gold standard" exams, but its recommendation was ignored by Education Secretary Ruth Kelly.