Pupils taking up places next year at a new city academy in London will have their lessons in temporary classrooms.
Buildings for the Oasis Academy in Enfield, north London, will not be ready because the costs of contractors are higher than had been expected.
The £21m academy will open as scheduled in September 2007, but Enfield Council said the situation was "disappointing".
Council leader Mike Rye has asked for a meeting with Education Secretary Alan Johnson to discuss finances.
Under Labour's high-profile academy scheme, the government adds about £25m for new buildings to each £2m donation from a sponsor.
The sponsor is then given wide-ranging freedoms to decide how the school is run.
Rev Steve Chalke, founder of the Oasis Trust which is developing the Enfield academy, said the price of construction in the South East of England was very high.
"We have to trim to keep in budget - this takes time and puts things behind the schedule you were otherwise hoping for," he said.
"The fact that we are opening in temporary accommodation rather than permanent accommodation is a direct result of the need to be accountable and deliver the scheme to budget in an environment where construction costs are rising rapidly."
The Oasis Trust is building four other academies - two in Lincolnshire, one in Bristol and one in Salford.
The Christian charity runs education, housing and healthcare projects in areas where people "lack opportunities and choice".
But Councillor Rye said the delay was "unacceptable".
"I have written to the education minister to express our dismay and I have requested an urgent meeting to discuss this issue.
"We have put significant resources into this project, and to discover that its first students will be taught in temporary accommodation is most disappointing indeed.
"You can be assured that we will continue to challenge the government over this problem and will continue to do all we can to support this exciting development in east Enfield."
A spokesman for the Department for Education and Skills said: "Following higher than expected costs from contractors we have provided further funding so the academy can open as planned in 2007.
"The temporary classrooms are of a very high standard and will provide a good learning environment while the academy is built."