The town hall has published plans to provide extra places at Allfarthing in Wandsworth, Sheringdale and Albemarle in Southfields, Hillbrook and Broadwater in Tooting, and Putney's Granard.

According to the latest population figures published by the Greater London Authority the borough needs a massive expansion in school places over the remainder of this decade to keep pace with the rapidly expanding school-age population.

The GLA data shows that Wandsworth's annual birth rate rose from 4,359 in 2003 to 5,477 in 2011 and is projected to continue rising in the years ahead.

Councillors were told this week that based on the current data the borough will need around 24 additional classes by September 2020 to ensure there are enough school places for local children.

The proposals for the September 2014 intake have been drawn up following detailed discussions with the headteachers and governors at all the schools where additional classes are being proposed. In total seven new reception classes are being planned, two additional ones at Hillbrook and one each at the remaining five schools.

Eight new classes will also be opening this September at the start of the 2013 academic year. This includes those being provided at the borough's three new free schools which are opening this autumn.

These are a two form entry school at the new Tooting Primary in Franciscan Road, sponsored by Graveney School, another two form entry at Rutherford House School in the former Balham Youth Court building, and a single form entry school at the South London Jewish Primary School, which will be opening temporarily at a local synagogue ahead of finding a permanent site.

Further proposals for yet more places are likely to be published later this year.

The council's education spokesman Cllr Kathy Tracey said: "The council is working hard to ensure there are enough school places for all the children that are being born in the borough.

"Over the last year we have invested close to £10m in creating extra classrooms at some of our best and most popular schools.

"And we have given our firm backing to the three new free schools that will be opening this September. These will provide additional places and also offer parents extra choice when it comes to deciding which local schools are the best for their children.

"However, demand for school places is projected to go on rising until the end of the decade. The rapidly rising birth rate is the main reason, but the growing reputation for academic excellence of Wandsworth's schools means they are attracting ever greater numbers of pupils.

"Ninety two per cent of our schools are officially rated good or outstanding and this means they are attracting parents from neighbouring boroughs and also parents who may have previously considered educating their children privately but now want to opt into the state system instead.

"Finding room for all the extra places we need is a real challenge, but one we are determined to meet in the best way possible. We are only considering extra classes at schools where additional pupils can be properly accommodated and where there is enough space to provide new classrooms."

The rise in demand for places is most acute in Furzedown, Tooting, Graveney, Earlsfield, Wandsworth Common, Northcote, Balham, Southfields, West Hill, East Putney, Thamesfield, West Putney and Roehampton wards.

To take part in the consultation and find out more information about what is being proposed visit the council's website.

The public consultation runs until Wednesday, May 22.