Authorities will also ask Tony Blair to intervene personally in their attempt to increase their say in the selection of heads, which currently falls entirely to school governors.
Without tight controls, they claim, standards could be jeopardised, despite Government moves to improve training forheads. Ministers have acknowledged that the management of a school is the key factor in its success.
However, the Bill, which will give local education authorities new powers to help drive up standards in schools, as well as creating a new schools framework, is expected to do no more than allow councillors to write to governors requesting a change of heart if they are unhappy about a choice of head.
LEA leaders insist the move does not go far enough, and are seeking powers to veto appointments they consider unsuitable or to approve shortlists of candidates.
The Local Government Association also wants selection panels to include two representatives from outside schools' governing bodies, including experienced governors from other schools or head teachers from other authorities.
LGA education chairman Graham Lane claimed that governors often ignored advice given by education officers. He said: "The Government is suggesting we write to governors and say `think again' when they have already made an appointment. But we want to get the appointment right first time."
LEAs themselves face takeover by Government "hit-squads", under today's Bill, if they are considered to be failing to drive up school standards.
The legislation will also pave the way for the creation of a new framework for schools, involving the abolition of Tory-created grant-maintained status.
Ministers were forced into partial retreat in October over plans for Church schools after bishops threatened to delay the Bill in the House of Lords. The concessions included an increase in the number of Church governors in aided schools.
The Tories will oppose the scrapping of GM status, claiming the move represents an onslaught on parental choice.