Under the new system all local authorities will get an increase in education funding of between 3.2 and 7 per cent per pupil. Ministers are anxious to ensure that the full increase is passed on to schools.
But the LGA says that its analysis of the funding settlement shows that some councils in southern England cannot afford to do so.
Essex is the worst hit authority with a funding gap of more than pound;7.5 million, followed by Kent (pound;3.7m) and Hampshire (pound;3.1m). All thirteen authorities are in London and the South-east, except Dorset.
Sir Jeremy Beecham, chair of the LGA, has written to Education Secretary Charles Clarke, ahead of a showdown meeting between council leaders and ministers on Monday, urging him to publicly rule out using a new power to set local authorities' education budgets.
The LGA fears some councils will be forced to make deep cuts in social services - another stated priority of central government - or increase council taxes "substantially".
A rise in pupil numbers in these areas, which mean that a 3.2 per cent increase in funding per pupil translates to a cash increase of 6.5 per cent is blamed by the LGA for the shortfall.
A spokesperson for the Department of Education and Skills admitted that some local authorities would find the settlement "disappointing".