Niall Bolger, chief executive of Sutton Council has written to all councils in London for support in asking the Department for Education (DfE) to change legislation limiting class sizes for five to seven-year-olds to 30.
In his letter, Mr Bolger said, "All London boroughs are facing unprecedented demand for additional primary school places."
"Increasing class sizes is not a Sutton Council policy or something that has been discussed at a political level," he said.
"There is a dreadful shortage of primary school places and we can't ignore the situation, especially when our schools, which are some of the best in the country, are attracting so many families."
Sutton Council is suggesting the maximum class size be raised to 32 from the cap of 30 introduced by the Labour government in a bid to reduce class sizes. But, as Mr Bolger explains, local councils are struggling to "meet their statutory obligations to educate all their young citizens within the financial envelope".
He added, "We do not wish to eliminate all parameters for class sizes but we consider 32 to be a pragmatic compromise between educational viability and financial prudency."
A DfE spokesman said: "The law remains clear that it is illegal for infant classes to exceed 30 pupils - no parent wants their child taught in a huge class.”
"We're dealing with the impact of soaring birth rates on primary schools - doubling targeted investment at areas facing the greatest pressure on numbers to over £4 billion in the next four years.”
"We are building free schools in areas where there are place shortages and letting good schools expand without limits to meet demand from parents."
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