In reading, which teachers said was a "kinder" test this year than in 2016, local authority results ranged from 61 per cent reaching the expected standard to 86 per cent. This is a range of 25 percentage points and the widest range of any of the subjects – but down from a gap of 29 percentage points last year.
Writing results, which are teacher-assessed, ranged from 67 per cent to 85 per cent reaching the expected standard. The gap has shrunk from 26 percentage points to 18.
And in maths, the range was from 67 per cent 88 per cent – a gap of 21 percentage points, down from 25 last year.
Last year, the local authority Sats scores exacerbated concerns about whether the moderation of writing had been consistent across the country. Rebecca Allen, director of Education Datalab, said then that it may be "safer" to judge schools on reading and maths alone. She highlighted the fact that some authorities had very high writing scores, taking into account their reading performance. In contrast, some other authorities had low writing scores, given their reading performance.
In response to these concerns, the government introduced mandatory training and a test for moderators – but Tes revealed earlier this year that two in three moderators had incorrectly assessed pupils when tested. And education secretary Justine Greening confirmed in July that schools would not be judged on writing, or any other single piece of data, alone.
'Pupils have responded well to the changes'
The statistics published today also show that 65 per cent girls achieved the expected standard in all of reading, writing and maths, compared with 57 per cent of boys.
Last year 57 per cent of girls achieved the expected standard in all of reading, writing and maths, compared with 50 per cent of boys.
The local authority results come after the national results were published earlier this year. These revealed that 61 per cent of children had reached the expected standard in reading, writing and mathematics – a rise from 53 per cent reaching the expected standard in the previous year, which had been the first year of the new Sats.
The school level results will be published in December.
Nick Gibb, school standards minister, said: "Today's results demonstrate that teachers and pupils have responded well to the new, more demanding primary school curriculum.
"Overall, the proportion of pupils reaching the expected standard has improved by 8 percentage points, with almost a third of pupils reaching the higher standard in the challenging grammar, punctuation and spelling test. Thanks to the government's reforms and the hard work of teachers, pupils are now leaving primary school better prepared for the rigours of secondary school."