The greatest progress is in maths, where scores have gone up by an average of 10 percentage points after last year's fall. English results have gone up by 5 percentage points.
The disappointment for David Blunkett, Education and Employment Secretary, who has pledged to resign if the targets for 2002 are not met, is that most of the improvement in English is through higher standards in the reading test.
Scores in writing, which lag well behind, have barely improved and show that fewer than 60 per cent of 11-year-olds are at the expected level for their age.
Maths shows a startling improvement over last year, even though the schools have not been required to teach a daily maths lesson until the beginning of this term. The Government estimates that 70 per cent of primaries began teaching the national numeracy strategy a year ahead of schedule.
The figures show that 70 per cent of 11-year-olds reached the expected standard in English, compared with 65 per cent in 1998. Standards need to improve at a rate of 3.5 percentage points annually for the Government to achieve the 2002 target of 80 per cent reaching level 4.
In maths, 69 per cent of 11-year-olds reached the expected standard, compared with 59 per cent last year. Scores fell by 3 percentage points in 1998, a result partly blamed on the introduction of new mental arithmetic tests. An improvement rate of only 2 percentage points a year is required to meet the national target of 75 per cent by 2002.
Mr Blunkett congratulated teachers and pupils, heralding what he described on Radio 4's Today programme as a new spirit in schools. He said: "These results show we were right to concentrate on the basics as we did.
"The sustained implementation of the literacy and numeracy strategies and the quality of training at the heart of the programmes have played their part."
Mr Blunkett said the focus in schools would be on writing. Teachers at the top end of primaries would be receiving extra training in the teaching of writing.
The results also record an improvement in the standard of spelling among seven-year-olds and smaller improvements in reading and writing.
However, secondary schools are not showing similar rates of improvement. Scores for 14-year-olds are largely the same as last year. In maths, scores are up by three percentage points to 62 per cent; scores are down 1 percentage point in science to 55 per cent and English scores are down 2 percentage points to 63 per cent.