In English tests the picture is not much better, with only 11 authorities reaching the 85 per cent target.
The figures show that each year around 120,000 11-year-olds still leave primary school unable to read or write properly - while nearer 150,000 have difficulty with maths.
However, inner-city schools in deprived areas have shown significant improvement. Not a single authority has more than 40 per cent of pupils unable to read, write or add up properly by the age of 11.
And the percentage of 11-year-olds achieving a level above the expected standard - the level of a 14-year-old - has doubled in English from 16 per cent to 32 per cent in the past decade. In maths, it has gone up from 18 per cent to 33 per cent.
Ministers acknowledge today's figures underline the need for further action to improve standards in the three R's in primary schools.
What galls them is that the dramatic improvements in some deprived inner-city boroughs show what they believe could be achieved if all schools made the same efforts. Today's tables, for instance, show that Tower Hamlets in east London - one of the most deprived boroughs in the country with more than half its pupils speaking English as a second language - beats the national average.
Eighty per cent of pupils reached the required standard in English and 78 per cent in maths - putting their performance above those of shire counties like Kent, considered "the garden of England", East Sussex, Norfolk and Suffolk.
The east London council invests heavily in education, using the Reading Recovery Programme, where those struggling to learn English get one-to-one tuition, to boost performance.
The targets, though, came under fire from education leaders for being "ridiculous".
"They were plucked out of the air and don't bear any relationship to the pupils in our schools," said Steve Sinnott, general secretary of the National Union of Teachers. "The Government has created a rod to beat itself with year after year. Pupil performance is improving but - inevitably, as with any investment in any area - that rate of improvement will slow as time goes by."
Nick Gibb, the Conservatives' schools spokesman, added: "Unless children master the basics... by the time they leave primary school, they will never be able to benefit from secondary education and their life chances will be blighted."
Slow rates of improvement have spurred ministers to overhaul the way maths and English are taught in primary schools.
In maths, children will be expected to have learnt their times tables by the age of eight to give them more time to understand how to tackle some of the harder questions they will face in the tests for 11-year-olds.
In English, the use of synthetic phonics to teach reading has become compulsory for the first time after research in Scotland showed many pupils who used this method had a reading age of 14 by the time they left primary school.
The Schools minister, Andrew Adonis, said: "Today's results show that we have come a long way since 1997, when a third of all 11-year-olds failed to reach the expected standard." But he added that despite the progress, "we are determined to redouble our efforts to help the one in five 11-year-olds who are still not reaching the standards required of their age in literacy and maths".
The 11 authorities that reached the 85 per cent figure in English are: The Isles of Scilly, Richmond, Bracknell Forest, Kingston-upon-Thames, Solihull, Barnet, Bromley, Harrow, Kensington and Chelsea, Surrey and Wokingham.
Raising the grades
Just two years ago Cobourg Primary School in Southwark, south London, was failed by Ofsted inspectors for its low standards, truancy and poor pupil behaviour.
But today the inner-city school is celebrating after being judged the best school for "adding value" to children's education - beating more than 17,500 others across England.
The school also ranked third most improved after more than doubling its 2003 results to well above the national average.
Julie Evans, the headteacher, brought in to improve Cobourg after it was declared failing in 2004, attributes much of its success to a drive to raise the expectations of both pupils and teachers.
"This is a very diverse area: 50 per cent of our pupils speak English as an additional language and 70 per cent come from ethnic minority backgrounds," she said. "Children join the school performing at below the national standard. But it does not matter what the deprivation of a school's catchment is. It is just not acceptable for any child not to achieve. That's why I wanted to work at Cobourg - because I thought that the children deserved better."
After a remarkable turn around, 90 per cent of pupils now achieve the required standard in maths and English and 92 per cent in science, according to government league tables published today.
England's most improved school was St Anne's RC Primary School in Ancoats, in inner-city Manchester, which made a 173 per cent improvement in English, mathematics and science over three years. Despite her school's success Suzanne Walker, the headteacher, admitted she was sceptical of government league tables.
"I feel strongly that league tables do not identify a good school or a bad one," she said.