In the 37 schools currently operating at more than 80 per cent capacity, three quarters of P1-3 classes and over a quarter of P4-7 classes are at or approaching the legal limit.

The figures have sparked concerns at a time when the council is axing three schools and raised fresh questions over the city's ability to meet Scottish Government pledges to cut class sizes.

The new statistics also show that there has been a 50 per cent rise in schools that operate waiting lists for P1 pupils – from 16 in 2007 to 24 this year.

Some of the most popular schools, like Sciennes Primary, have nine P1-3 classes consisting of 22 or more children. The legal limit is currently 25. Sciennes also has eight classes in the P4-7 year groups consisting of at least 30 children, when the legal limit is 33.

The new class-size statistics were released after Labour councillor Angela Blacklock became concerned about growing class sizes and asked education bosses for figures.

She said: "I'm shocked at what's happening, and I would like the convener to admit that class sizes are rising in Edinburgh."

It emerged earlier this year that it would cost the city £24 million to meet the SNP's manifesto pledge to reduce P1-P3 classes to 18 pupils.

A report published in May revealed that just nine per cent of P1-P3 classes had 18 or fewer pupils, and £7.7m a year would be needed to pay for more teachers to achieve the goal.

But Tina Woolnough, chair of Parents in Partnership, believes there is no excuse for rising class sizes and is calling on the council to produce "robust" measures to tackle the problem.

She said: "I haven't heard of specific plans to address the class size issue, and I don't know how hard the council is trying.

"There has been a reliance on the pupil roll falling to enable smaller class sizes, but clearly that's not going to happen universally across the city."

Councillors voted last week to close three primaries – Lismore, Bonnington and Westburn – because of falling pupil numbers in the city.

Maggie Paterson, chair of Lismore's parent council, said it was "disgusting" that the council is closing schools when some primaries are struggling to cope.

A council spokeswoman said: "The number of children at a particular school is determined by a range of factors, including the number in the catchment area at the P1 enrolment stage and the size of the building.

"For parents and carers who wish to send their child to a school outwith their catchment area, we follow Scottish Government legislation that allows parents to state a preference about where to send their child to school."