The Headteachers Learning and Management Programme, Headlamp, will be run by the new Teacher Training Agency with Pounds 2.74 million removed from local authority education budgets.
John Fowler, assistant secretary at the Association of Metropolitan Authorities, described the move as "quite outrageous".
News of the funding arrangements only emerged in a written answer to a parliamentary question.
The decision, said Mr Fowler, effectively prevents LEAs from running headteacher training programmes, even though there has been neither consultation nor public discussion of the matter.
"The DFE now considers that local authorities have no responsibility for the training of headteachers. I'd like to know how much is going to be taken from grant-maintained schools. Are they going to pay their share?".