Thousands of five year olds began their first day at school this week, but a new report shows demand for primary schools places is far outstripping the spots available.

Figures released by the Local Government Association (LGA) reveal that in May 2012 there were only 17,531 primary school spaces available this academic year and 17,949 children needing a place.

Despite the opening of three new three schools this week, as well as 25 new reception classes across the borough in the past three years, Wandsworth Council is facing a race against time to continually provide for spiralling population increases.

Altogether there were 3,052 places available for this year's intake of children for parents seeking state school education.

Children in private education or send attending schools outside the borough reduce the shortfall problem.

Wandsworth Council said every child has been offered a place somewhere, a statutory duty for local authorities, but accepts the problem is only likely to escalate.

Free schools Tooting Primary School, Rutherford Primary School and the Mosaic Jewish Primary School opened this week taking in 90 children.

But the council has admitted there is huge pressure for primary school places, with an extra 1,632 more schoolchildren needing a place this year since 2011.

The number of children expected to need a reception class is expected to rise by 15 per cent in 2016, with demand across all primary places expected to jump to almost 20,500.

Wandsworth Council is looking to expand primary schools to meet demand.

Hillbrook, Allfarthing, Sheringdale, Albemarle and Granard primaries could all expand by next September, with an additional class in Allfarthing at the start of the 2015.

A further two new primary schools are being planned to accommodate 420 pupils in the derelict Putney Hospital site and the Atheldene Centre in Earlsfield.

Councillor Kathy Tracey, cabinet member for education, said: "These figures from the LGA very clearly demonstrate the pressure that is building on school places.

"Over the next three years something like an additional 2,500 reception places could be needed in this borough if we are to offer places to all the children that need them.

"We have already expanded some of our best performing and most popular schools and we will be working hard in the coming months to ensure we have sufficient classroom places to meet this rising demand."

Leader of the opposition party, Councillor Rex Osborn, said: "Parents will be very concerned by these figures.

"We have known about a baby boom in the borough for some time and the council should have planned ahead.

"It doesn’t help that the Tories have closed 10 local primary schools since 1990, many of which were sold for property developments."