Education Secretary Ruth Kelly has outlined plans to encourage all England's schools to be "autonomous".
The Education White Paper says councils should become parent "champions", mediating between them and head teachers, rather than being providers.
Parents also had to contribute "much more fully", while "coasting" schools would be tackled, Ms Kelly told MPs.
But shadow education secretary David Cameron, who backed some ideas, said other parts were a "complete muddle".
Liberal Democrat education spokesman Ed Davey said it was central, not local, government which was "stifling variety".
The white paper would allow all secondary and primary schools to become "trust" schools, which could handle their own admissions according to national guidelines.
Trusts - which could run individual schools or whole chains - could be backed by charities, faith groups, businesses or parents' groups.
WHITE PAPER - KEY POINTS
All schools can be run by 'trusts', with parents, businesses, faith groups and charities taking part
Schools commissioner to oversee setting up of trusts and matching them to schools
Councils to become pupils' 'champions'
Bus subsidies for poorer children
Failing schools to 'federate' with better ones
'Easier' for independent schools to 'opt in' to state sector
Meanwhile, independent schools would be allowed to "opt in" to the state sector.
Opponents of the reforms say children from the poorest backgrounds will suffer, with middle-class parents benefiting most from extra powers.
Deputy Prime Minister John Prescott has reportedly raised objections that the proposals will damage Labour's traditional policy of comprehensive secondary education.
The white paper puts forward a new "schools commissioner", to decide whether trusts can start, identifies backers and matches them up.
Buses could be subsidised to allow children from poorer families to travel further afield for an education.
Ms Kelly, who got big cheers from Tory MPs throughout her speech, said all schools had "to deliver radical improvements in standards and the flexibility to create real centres of excellence".
Failing schools would be told to "federate" with better ones. Ms Kelly also said streaming should happen in all secondaries.
The white paper, supported in large part by the Conservatives but opposed by some Labour backbenchers, encourages parents' groups, charities, faith groups and businesses to start up schools.
Mr Cameron said the white paper represented a return to grant-maintained schools, introduced by the Conservatives but abolished by Labour.
Mr Davey said schools needed more freedom from Whitehall, more teachers, reform of the curriculum and for lower pupil-teacher ratios.