Pupils from the poorest backgrounds in England achieved their best-ever results at the end of their primary school education this year, as well as narrowing the gap in attainment between themselves and their peers from wealthier families.

Schools such as Bygrove primary school in Poplar, east London, achieved outstanding results in key stage 2 tests of literacy and numeracy, according to nationwide figures published on Thursday by the Department for Education (DfE). More than 80% of Bygrove’s pupils come from disadvantaged backgrounds and English is a second language for many of them.

Overall, 67% of pupils from disadvantaged backgrounds – meaning that they had received free school meals at some point – achieved the government’s targets in maths, reading and writing, compared with 61% in 2012, and closing the attainment gap by two percentage points in the space of a year.

Nationally, 79% of pupils reached the DfE’s targets for reading, writing and maths – with more schools reaching the government’s benchmarks for success, despite a more challenging mark being set this year.

A total of 768 of England’s nearly 16,000 primary schools failed to reach this year’s target of 65% of pupils achieving the required standard, the same proportion as last year. Had last year’s target of 60% been applied, just 469 primaries would have failed this year.

News of the improvements came the day after Sir Michael Wilshaw lavished praise on the performance of England’s primaries, in contrast to the progress of state secondaries, which the Ofsted chief inspector described as being stalled.

The schools minister David Laws said he was pleased that primaries had responded so well to the higher standard.

“It is also encouraging to see the attainment gap between disadvantaged children and their peers continue to narrow and parents, teachers and pupils deserve to be congratulated for their efforts. But we know there is more to do and there are still too many areas with simply unacceptable levels of attainment for disadvantaged pupils,” Laws said.

The key stage 2 results – standardised tests of reading and maths taken by 11-year-olds, along with assessed writing grades – were also taken for the first time by several free schools. The published results from the nine free schools showed little variation from national averages.

Among the handful of established schools that could claim to be the best in England, depending on the criteria, were Newton Farm infant and junior school in Harrow, and Fox primary school in Notting Hill, London.

Primaries in London were among the best-performing overall, but local authorities such as Blackpool, North Tyneside and St Helens were also among the top performers. The list of top 10 local authorities was dominated by inner and outer London, with the single exception of the borough of Trafford in Greater Manchester. In the worst-performing areas, Doncaster, Bradford and Wakefield were among those with the lowest percentage of successful primaries, alongside Luton, Peterborough and Bedford.

Disadvantaged pupils in the capital did better than their peers elsewhere. In Tower Hamlets (Bygrove primary school’s local authority) nearly 70% of pupils had qualified for free school meals, and 80% reached benchmarks in the key stage 2 results. The neighbouring borough of Newham, however, had a smaller attainment gap of just three percentage points between disadvantaged and better-off pupils.

Poole, in Dorset, recorded the worst performance by disadvantaged pupils, with just 53% reaching the expected pass mark in reading, writing and maths – compared with 78% of their schoolmates. Poole was worst overall, with 27% of its primaries failing to reach the 65% benchmark.