The gulf between the strongest- and weakest-performing primary schools in England widened this year, according to national results from key stage 2 tests of literacy and maths taken by 11-year-olds in spring.

The widening gap was driven by improved performance among local authorities such as Richmond-upon-Thames, where 80% of pupils met the expected standards in reading, writing and maths, compared with the national average of 65% of pupils in mainstream schools.

While the results showed an improved performance overall, substantial variations remained between local authorities, while girls continued to maintain or extend their edge over boys in reading and writing abilities.

In the third year since the new standardised tests were introduced in 2016, the proportion of pupils reaching the government’s expected standard continued to improve, with this year’s cohort of 600,000 pupils the first to have been taught the full revised national curriculum.

Nick Gibb, the minister for school standards, said: “Schools have adapted to the higher expectations and greater challenge of the new primary curriculum. In the first Sats that tested pupils’ achievements, in 2016, just 66% reached the expected standard in reading. Today that figure is 75%.”

The gap in attainment between the best and worst was 28 percentage points, between Richmond and Peterborough, where 52% of pupils reached the expected standard in the three tests. In 2017 the gap was 25 percentage points.

Schools in inner and outer London received the highest scores overall, including 73% of pupils in Newham reaching the standards and 71% in Tower Hamlets, two of the most deprived local authorities in England. Outside London, 75% of pupils in Trafford schools reached the national standards, as did 71% of pupils in Redcar and Cleveland and 70% in Gateshead.

The statistics showed that 10% of pupils reached the higher standard in reading, writing and maths, compared with just 5% three years previously.

Girls remained the strongest performers across all subjects. In reading, 32% of girls achieved marks that showed them to be working at a higher level than the national standard, compared with 25% of boys.

In maths, girls were a single percentage point ahead of boys in reaching the national standard, and more boys were marked as performing at a higher level, the single category where they outperformed girls.

Local authority-maintained schools did slightly better than those with academy status, although there remained a clear divide between those schools that voluntarily converted to academy status and those that were taken into sponsorship.

Individual school-level data will be published by the Department for Education in December.