Schools which had failed or been labelled struggling also featured near the top of the table for the most improved primaries.
Stephen Twigg, education minister, said he would discuss the results revealed in the key stage 2 performance tables with inspectors.
London schools dominated a list of the primaries where pupils make the most progress in their learning between seven and 11.
The capital had nine of the top 10 local authorities in a "value-added" measure of key stage 2 tests.
Mr Twigg told The TES: "It's fair to say that in some parts of London, schools have lagged behind (in the tests). This could be London schools catching up."
The top-performing schools in England on the value-added calculation were Heath Mount primary, Birmingham, and Orrets Meadow, in the Wirral, while Kensington and Chelsea, west London, were the top-performing council areas.
Sherington primary, in Greenwich, east London, was the country's most improved school, while Pirton, in Hertfordshire, and St Michael's, near Rochdale, were the top performers overall.
Nationally, 78 per cent of pupils achieved the expected level 4 in English.
The figure for the past four years was 75 per cent. For maths, the figure was 74 per cent, up one point, but in science there was a one point drop to 86 per cent.
Pupils' average test achievements in 24 councils have fallen since 2001, the tables showed.