Provisional results for local education authorities in key stage 2 tests show that, although nationally there was a single percentage point increase in the number of 11-year-olds reaching level 4 in English and maths, the local picture was more varied.
English scores rose in 109 local authorities and fell in 14 others. Maths results rose in 96 authorities and fell in 30.
North Somerset had the biggest rise in English, up six points. Telford and Wrekin had a rise in maths of six points. Richmond-upon-Thames is still top of the list, with 88 per cent of pupils reaching level 4 in English, and 85 per cent of them reaching it in maths.
It is the only authority in which at least 85 per cent of pupils reach level 4 in both subjects - the Government's target for next year.
Results for Southwark, in south London, rose by four points in English to 72 per cent and by three points in maths to 67 per cent. These results take it from bottom place last year to sixth from bottom. Southwark schools predicted they would reach 71 per cent in English and 72 per cent in maths, although the council targets were 76 per cent and 75 per cent respectively.
Terry Reynolds, Southwark's deputy of director of education, said: "We have no quarrel with the targets - they should be achievable. We are closer to them and aim to be closer next year.
"Southwark has a high level of children who face challenges. Schools have a difficult job and what they need is constantly good teaching."
Hackney, in east London, finished last, dropping two points in both English and maths, to 68 per cent and 65 per cent respectively.
Results published this week for prep schools show 98 per cent of pupils achieved level 4 in English, compared with 79 per cent nationally. In maths, 95 per cent achieved level 4, compared with 75 per cent nationally.
Just 250 private schools - less than half of those in the Incorporated Association of Preparatory Schools - chose to sit the tests. More than half of pupils reached level 5, the standard expected at 13. Nationally, fewer than a third of children reach this level at the age of 11.
At Alleyn's junior school in Dulwich, south London, where the fees are Pounds 7,750 a year, all pupils reached level 4 and 87 per cent reached level 5 in maths. Head Mark O'Donnell is still waiting for confirmation of the English result, but expects it to be around 90 per cent of pupils reaching level 5.
He said: "The national tests are well written and provide a national standard against which schools can judge how well they are teaching. It is not about league tables, but about teaching good basic skills."