Will local comps suffer as grammars expand?
They say that the plans, announced by schools minister David Miliband, could allow grammar and faith schools to take students away from local comprehensives which may then be forced to close.
Heads and council leaders also said the proposals would undermine collaboration between schools and warned that standards could fall as a result.
Details of the plans, which were part of last year's Education Act, were published by the Government this week.
New guidance instructs local school organisation committees to approve the expansion of successful schools "unless there is evidence it will have a damaging effect on standards overall in the area".
Ministers have promised that expanding schools can get up to pound;500,000 for building work.
Any school can publish proposals to expand and private, voluntary, faith and community groups will be given the chance to run new schools. Local authorities will be expected to allow "open competitions" between groups wanting to run schools .
Mr Miliband said: "We are determined to give more pupils and parents the chance to attend high-quality schools, therefore we are making it easier for popular schools to expand."
But Graham Lane, education chair of the Local Government Association, said:
"This is a waste of money. You will finish up closing schools which lose out on pupils and then build new ones to replace them. It is certainly not going to raise standards and could do the opposite."
Margaret Tulloch, spokeswoman for the Campaign for the Advancement of State Education, said the policy would benefit those "who shout loudest", including grammar and faith schools.
Damian Green, shadow education secretary, said: "The Government is inching towards acceptance of Conservative policy on these issues, but is still afraid to be bold."
Details relating to competitions for running new schools can be found at www.dfes.gov.ukschoolorg