Labour's manifesto pledge to cut class sizes will be sorely tested in Kingston-upon-Thames where seven out of 10 pupils are taught in lessons of more than 30.
There is no spare space in the primary schools in the borough, one of the top 10 performing authorities in this year's tests for 11-year-olds.
John Braithwaite, education director, estimates the council would need another 48 classrooms to fulfill Labour's promise to cut class sizes to 30 or under for every five, six and seven-year-old. He said: "We want the resources to meet our particular problem."
Schools in Kingston draw children from Surrey, Sutton, Merton, Wandsworth and Richmond and headteachers are already concerned about the potential loss from their budgets that would follow cuts in pupil numbers.
This year they needed Pounds 2 million to cater for the extra pupils expected to start school in September, to fund the teachers' pay award and cover inflation. However, the Liberal Democrat-controlled local authority was only able to find Pounds 300,000.
Caroline Egerton, a mother of three and chair of governors at two schools in the borough, said: "Parents would be thrilled if classes were cut.
"Our schools do so well in the league tables because we are a very leafy borough and have an incredibly imaginative teaching force which is very hard-working."
Official figures show 13 English LEAs now have under 10 per cent of primary pupils in classes of 30 or fewer while only one (the Isles of Scilly) is in the top 10 of the key stage 2 league table.
There are already more than 1.1 million children in classes of 31 to 35, a further 120,354 in classes of 36 to 40 and almost 9,500 in classes of 41 or more.
Civil servants are struggling to turn the class size promise into reality and are worried about how it will be funded and implemented. They believe the pledge can only be met through paying a specific grant to local authorities and fear that money given to schools to cut class size could be spent elsewhere.
Local authority leaders want councils to draw up plans immediately to reduce classes in return for endorsement by the Department for Education and Employment, with money released in phased instalments from September.
They now want a joint DFEELocal Government Association working party to monitor progress and look at changes to local management schemes, admissions regulations, the Greenwich judgment and standard number requirements.
Graham Lane, the LGA education chair who met Mr Blunkett this week, said classes over 30 should attract only marginal funding for every child over the limit instead of the full pupil-weighted amount.
Class sizes have been rising steadily in primary schools despite attempts by LEAs to pump more money into them. Local management of schools means that heads and governors set their own spending priorities.
The previous government was just beginning to grasp the difficulties local management posed, according to civil servants. "LMS at present is not terribly satisfactory because its not a very good vehicle for delivering your policies, " said a DFEE source.
Labour expects to fulfil its class size pledge within five years and insists that no money other than that saved from the abolition of the Assisted Places Scheme will be used to do so.
Good schools are undoubtedly popular with parents and the primaries heading the key stage two league table have at least 20 per cent of their pupils in classes of 31 to 35. Schools at the bottom of the league table mostly had under 10 per cent of pupils in classes of more than 30.