The education secretary is being urged to ditch regulations limiting infant class sizes to 30 pupils, in order to save money.
Sutton council chief executive Niall Bolger said his council had spent £7m on accommodating the extra pupils its schools would admit in September.
He said the limit could be raised to 32 without harming education.
But the government said no parent would want their child taught in a huge class.
The introduction of maximum sizes for infant classes was introduced in 1998. It was one of the incoming Labour government's five key pledges before the 1997 general election.
It followed research which suggested younger children did better in smaller class sizes, as they began to learn the basics of literacy and numeracy.
Mr Bolger said all London boroughs faced unprecedented demand for additional primary school places.
He argued that the rules on maximum class sizes were introduced at a time when there were surplus places and a lower population level.
But now, he suggested, as councils tightened their belts, many were 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."
Mr Bolger has written to all London chief executives asking them to support such a move.
He said Sutton, like many councils, had been funding additional classes over a number of years and that all the easy options had been exhausted. Thus, extra costs had increased to £7m for 2012.
"However, class sizes had been expanded to 32, none of this expenditure would have been required - a considerable saving to the public purse and without undue detriment to children's education," he added.
But Councillor Peter Walker, Merton council's cabinet member for education, said: "Increasing class sizes in our schools at this time is shortsighted, will threaten school standards, is unfair to our children and will endanger our economic prospects.
"Don't do Michael Gove's dirty work for him."
A Department for Education spokesman said the law remained clear that it was illegal for infant classes to exceed 30 pupils.
"No parent would want 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 £4bn in the next four years.
"We are building free schools in areas where is are place shortages and letting good schools to expand without limits to meet demand from parents."
The government's new admissions code allows the limits to be exceeded so that twins may be admitted to the same class or children of servicemen may be given a place.