The rise of one percentage point in all three subjects comes after the literacy and numeracy frameworks were renewed this year to bring in more speaking and listening and to get through basic maths earlier.
But the gap between children's ability in reading and writing means that only 66 per cent of pupils reach level 4 in both papers, and only 60 per cent reach level 4 in reading, writing and maths.
In English, boys narrowed the gap on girls. Seventy-six per cent reached level 4, a rise from 75, while girls' results remained static at 85 per cent.
Boys' writing has shown the biggest improvement of any test score up five percentage points in the past two years. But their results are still a long way behind girls. While there are just seven authorities in which fewer than 67 per cent of girls get level 4 in writing, there are 11 authorities which have boys at this level.
The Government's synthetic phonics programme, Letters and Sounds, has been sent to schools to boost early reading standards. The renewed literacy framework includes strategies aimed at improving boys' writing, such as planning and organising a piece of writing before starting it, creating a series of literacy lessons around a single theme lasting one to three weeks and guided writing, in which the teacher demonstrates a particular skill.