Education leaders today praised the hard work of children and teachers as well as efforts to spread best practice to all city schools.

There has been a dramatic turn around at some schools in recent years.

At Niddrie Mill Primary for instance, only a third of pupils passed their maths tests in 2003, but now almost three-quarters are up to speed. The school has also seen similar improvements in reading, and, to a slightly lesser extent, in writing.

At St Catherine's RC Primary in Gracemount, three-quarters of children now pass their maths tests, with pupils also achieving dramatically improved pass rates in reading and writing. Six years ago, less than half the children there passed in each of the three Rs.

There has been much less clear change at the higher end, where some schools were already achieving almost perfect pass rates in 2002.

But concerns have been raised about the high numbers of children still leaving primary school without the basic skills.

A third of pupils across the primary school age range failed their tests in reading, writing or maths in 2008, while just over a quarter of schools are still struggling to meet the minimum levels.

And in one in ten schools – including the closure-threatened Westburn Primary – a third of all pupils are failing to meet the basic standards in all of the three Rs.

The results are contained in a newly published report which shows gradual progress has been made over the past six years in raising core skills.

The lessons learned at schools which made the biggest improvements are now to be passed on to teachers across the city.

Councillor Marilyne MacLaren, the city's education leader, said: "This is testament to a great deal of hard work by teachers and pupils alike. However, it is important we do not become complacent, as there is still a lot of work to be done for under-achieving children to narrow the divide between the highest and lowest achievers.

"Officers look at schools where attainment figures have improved markedly to learn from them and then apply the good practice to schools across the city."

The top performing school is St Peter's Primary in Morningside, where 98 per cent of pupils have met or exceeded minimum standards in reading and 96 per cent in writing.

At Bonaly Primary School, 98 per cent of pupils gained the basic maths skills, making it the top performer in that subject.

On average, pupils in Edinburgh's primaries are performing well, comfortably meeting the nationally-set minimum standards. A total of 84 per cent of pupils are achieving or exceeding the basics in reading and maths – both up from 82 per cent last year – while 77 per cent of children are making the grade in writing, which is also a two per cent rise from 2007.

Among the schools expected to receive extra support are Royston Primary and the closure-threatened Lismore and Westburn primaries, which have the worst results for maths, writing and reading respectively.

Councillor Ricky Henderson, Labour's education spokesman, said he was concerned about the attainment gap between the better performing schools and some of the others.

He said: "The general improvement is to be welcomed. However, there is still a concerning disparity between the better performing schools and the poorer ones.

"I'm not a great fan of league tables because they don't reflect all the things that go on in a school, but obviously you want children to be able to read and write before they go to secondary school."

The improving primary school results follows other good news from the Capital's schools.

The number of high school pupils who are achieving good grades in their exams is also on the increase, with students in the Capital outperforming the Scottish average in the Higher exams sat in May.

The number of pupils who got good Standard Grade results is also higher than it has been for the past six years. The number of Higher passes among fifth year pupils has risen by more than 250, while those gaining three or more Highers has risen by two per cent. In addition, 19 out of the city's 23 high schools have seen an increase in the number of pupils passing at least three Highers between 2006-07 and 2007-08.