Local authorities with a high level of provision for young children "have nothing to gain and everything to lose" from the new scheme, said Alan Parker, education officer of the Association of Metropolitan Authorities.
His chairman, Graham Lane, warned that a good service could be destabilised, and provision for three-year-olds could be threatened.
The Government says the scheme will be "cost neutral" for local authorities, since Pounds 1,100 will be "top-sliced" from their standard spending assessment for each four-year-old in the state sector, and brought back to the LEA as vouchers by parents.
The more places an LEA provides, the more cash is top-sliced. However, if any parents take their vouchers elsewhere, that money will be lost to the state sector, and this could raise the cost of state places.
LEAs, says the Government, will keep the remainder of their existing funds for four-year-olds, "so they will still be able to provide as many full-time places in nursery schools or nursery classes as they do now". LEAs will be expected to provide for children with special needs.
A local authority such as Cleveland, which has a place for virtually all its four-year-olds, cannot add much to its schools' budgets through the voucher scheme, but it expects to break even because few parents there could afford private education.
Rural Gloucestershire, with little nursery education, could theoretically gain some Pounds 2 million a year if it boosted the places for four-year-olds to 100 per cent - although this would be difficult because children are too scattered to create cost-effective classes without large-scale bussing. The LEA has the equivalent of two-thirds of its 6,000 four-year-olds in reception classes averaged out over a year, as well as about 400 in family centres. All but 5 per cent of the rest are in playgroups.
"We are going to have to evaluate the options," says deputy chief education officer John Braithwaite. He said they would co-operate with the local playgroup organisation.
Graham Lane said: "The biggest LEA providers of nursery education target the most needy families and offer a nursery place from the age of three. Diverting cash from these LEAs to fund a scheme for four-year-olds . . . will threaten the youngest and most needy children."