They passed a motion at their annual conference in Brighton saying that the scheme was impractical and threatened to reduce rather than increase the number of nursery places.
The future of the scheme, announced by Gillian Shephard, the Secretary of State for Education and Employment, two weeks ago, depends on next year's pilot scheme in which authorities have been invited to take part. She is planning to give parents of all four-year-olds pounds 1,100 vouchers to spend at a private or local authority nursery or a playgroup.
Geoff Wright from Solihull, leader of the Conservatives on the Association of Metropolitan Authorities education committee, said: "We all want to improve nursery provision but you will not improve it by top-slicing the grant going to authorities who already make that provision."
A spokesman for the association said authorities were not threatening to boycott the pilot - they simply could not see any advantage in taking part.
Don Foster, the Liberal Democrats' education spokesman, urged Lib Dem councils not to participate in the pilot scheme, which Mrs Shephard hopes will involve 10 per cent of four-year-olds. He said the voucher scheme was "a middle class bonanza transferring public subsidy from the poor to the rich".
Robin Squire, the schools minister, said: "A number of authorities have already made firm expressions of interest in being included in the pilot scheme. A boycott would be pointless and self-defeating since all parents for four-year-olds will receive such vouchers from April 1997 anyway."
At least one Conservative local authority, Wandsworth, is known to be interested, but it already has plenty of nursery places for four-year-olds.Reuse content