The national picture will not emerge until figures are published this autumn, but it is likely that at least 80 per cent of 11-year-olds have reached the required standard.
Results in science are better than in English and maths, where the greatest effort is being put in to raise standards.
Schools such as St Joseph's Roman Catholic primary in North Yorkshire have managed to get all their pupils to the target level 4 in science - an improvement of 25 percentage points.
Head John Fullen believes his results are probably a reflection of the fact that children are now more aware of what is equired.
"We don't set much store by the tests because they can't test children's understanding of science, only their knowledge," he said.
But Rosemary Feasey, lecturer in primary science education at Durham University, said the tests did more than make children recall facts. She said:
"In this year's test there was greater focus on scientific inquiry, collecting data and interpreting information.
"I think primary science in recent years has been a success story, though I don't think the tests necessarily prove that one way or the other," she says.
Last year, 78 per cent of 11-year-olds reached the target standard, a nine percentage points improvement on 1998.