Manchester King David chiefs fear the schools will lose out because of the government's much-trumpeted pupil premium commitment.
The scheme will target extra funding to schools based on the number of pupils eligible for free meals - a measure of poverty. The anticipated consequence is that schools with few pupils from poor families will receive less money.
King David High governors' chair Joshua Rowe says that as KD parents tend to be more affluent, the schools could be £1.8 million a year worse off in comparison to other Manchester schools.
"The difference between what we get and what a comparable school - with many more free school meals - gets equates to as much as around 40 per cent [of our budget], which is mega.
"It is unfair because children at the upper end of the academic scale have as many special needs as those at the lower end. To denude them of the resources and facilities they deserve is a travesty. Worse, it is a way of ensuring that we stifle the potential for excellence and achievement which is the ultimate investment in our future."
Mr Rowe has written to Education Secretary Michael Gove criticising the plan. He has also conveyed concern over budget cuts to Manchester Local Education Authority.
"We have no idea what cuts there are going to be," Mr Rowe added. "We are going to be launching a King David appeal shortly because we have to find £2 million for the new buildings."
King David was given £22 million of public money to rebuild its school. It has escaped the 40 per cent funding cuts on building projects because of the advanced stage of construction. But KD had pledged to find £2 million towards the project.
Manchester City Council says it is not yet ready to release information about the scope and timing of funding cuts.