Nor does the curriculum appear to have raised standards in primary school literacy, he says - although there is no evidence of a new education "crisis", because the tests are incapable of comparing pupil progress year by year, despite their Pounds 34 million cost.
In his presidential address at the BA's annual meeting in Birmingham University, Professor Campbell, from Warwick University's Institute of Education, called for the re-establishment of the Government's Assessment of Performance Unit, and for a new set of centrally approved texts to accompany the national curriculum - as used in more successful countries.
"The first priority must be to re-establish a national monitoring unit, ideally at arm's length from the Department for Education and Employment, to conduct regular, reliable and relatively objective surveys of standards, " he said. "Without such a unit it will remain possible in the future for politicians and others to assert a crisis in education with no one knowing for certain whether it is real or manufactured.
"No one, not even Prince Charles or Tony Blair, actually knows whether standards of literacy and numeracy have improved, remained the same or deteriorated since the introduction of the national curriculum. To arrive at judgments we are far too heavily dependent on evidence produced for, and often controversially interpreted by, official sources.
"It remains immensely puzzling to me why a government which I believe to be genuinely interested in raising standards in primary education closed down its own well-regarded and effective monitoring unit at precisely the point when, had it been kept open, it could have started to collect reliable evidence of the impact of the educational reforms on standards."
Professor Campbell said that over-ambitious testing plans in the 1980s lay at the root of the problem: the first national curriculum tests were designed to show both pupils' progress and their attainment in relation to others. They proved unworkable and were simplified to concentrate on attainment.
"We have a lot of evidence about differences in standards of attainment, but rather less about differences in progress," said Professor Campbell. "Yet it is progress that we really need to know about, if we are to judge the effectiveness of schools and teachers."
There is no evidence that the national curriuculum has helped either maths or literacy, he said. "I can see little evidence that the introduction of the national curriculum has had a significant positive effect." But there is no justification for the view that there is a general crisis in reading standards. "The overall picture is of at least moderately effective teaching in around 80 per cent of schools."
The prospect of a new national monitoring unit was immediately attacked by chief inspector Chris Woodhead. Replying to Professor Campbell's speech, he described it as an increase in bureaucracy and "a waste of taxpayers' money", saying that national monitoring should be carried out by his own department, the Office for Standards in Education, within its existing budget.