Schools are spending tens of thousands of pounds more a year to meet rising costs of contracts with private firms.
These Private Finance Initiative (PFI) schools are locked into 25- to 30-year contracts in which charges go up by the highest measure of inflation.
One school said "rigid" and "specific" demands set out in its PFI contract now cost almost 20% of its budget.
PFI investors say the contracts are long-term value for money for taxpayers.
More than 900 schools in England were built through PFI contracts, with the first opening in 1999. The initiative was scrapped in 2018.
These state schools are owned and maintained by the private sector during the contract, until taxpayers' money has repaid the debt and the buildings go into state ownership.
PFI costs go up by the Retail Price Index, a typically higher measure of inflation which is no longer used by the government as an official national statistic.
The terms of PFI contracts are routinely covered by non-disclosure agreements - but some head teachers are now speaking out.
Middlefield Primary in Speke, Liverpool, opened after the local authority entered a PFI agreement for new school buildings.
Head teacher David Potter says nearly 20% of the school's entire budget is now spent on meeting "frustrating" terms of the PFI contract - squeezing what he can spend on classroom staff.
All of the maintenance, catering and cleaning for the school is included in the PFI contract which will cost more than £470,000 this year - a rise of more than £151,000 since 2021.
The contract sets out in precise detail how the school must be maintained, including that the playing field grass must not grow more than 2.5cm high.
"We're in the middle of February, the ground's a bit waterlogged, so we won't use this space very much at this time of year," Mr Potter says.
"But come rain or shine every week, the grounds maintenance team come out and they cut this field.
"We should have the freedom to say, actually, we think we can do without."
Maintaining the field costs the school around £30,000 a year.
The contract does not allow the school's head teacher to shop around for better prices from other suppliers - something Mr Potter finds "incredibly frustrating" as he watches prices rise.
Such costs have forced him to make savings elsewhere. Four members of classroom staff have not been replaced since 2020.
The PFI company told the BBC it would be willing to renegotiate for the grass to grow to 5cm, but Liverpool City Council said the legal costs would outweigh the benefits.
Ten other PFI primary schools in Liverpool have provided figures showing similar price rises.
'You feel like a failure'
Costs are also spiralling for Glyn Potts, head teacher at Cardinal Newman College in Oldham, a large secondary school that was opened in 2012.
But he is most concerned by the state of the building. Since pupils moved in it has been beset by problems with the roof, leading to hundreds of thousands of pounds being withheld from payments to the private contractor.
Children were sent home in 2021 after problems with the heating system led to radiator pipes bursting - spewing "red-hot" water and repeatedly flooding classrooms.
"When a radiator bursts in a school, the ferocity of the water will arc three or four foot up," Mr Potts says.
At times, radiator bursts meant up to 60% of the school was cut off.
In order to get the heating system replaced Mr Potts had to ask the council to argue with the contractors.
Speaking to the BBC, he put his head in his hands as he said: "I have to go to those parents and say I'm doing the very best by them with no impact.
"You feel like a failure."
When we returned a few days later, water gushed through the roof of a classroom when its ceiling collapsed as maintenance contractors tried to fix heating on the floor above.
In ceiling spaces around school corridors, large plastic tubes are visible to collect roof leaks.
Other head teachers in England told us they had been advised against speaking publicly about the pressures PFI costs are causing, because of non-disclosure agreements that are built into the contracts.
Last week, Stoke City Council held a meeting in private with the 88 PFI schools in the city which were warned they face "double digit" percentage increases in their PFI costs within weeks.
Stoke's PFI contract, which includes the largest number of schools, will be among the first to come to an end in October 2025.
The BBC has seen notes of the meeting and spoken to people who attended, although the public were excluded.
Meg Hillier, chair of the Public Accounts Committee of MPs, which looks at value for money from taxes, told the BBC the secrecy around these contracts was "ridiculous" and "unacceptable".
"If there was more openness, the publicity would shock many citizens and taxpayers, and that might push the companies to think again and make sure they're not wringing every last penny out of our school system," she said.
The Department for Education said it was increasing support for schools in PFI contracts by 10.4% in the coming financial year.
Speaking on behalf of PFI investors, Lord John Hutton said price comparisons were made regularly, but school budgets had not kept up with inflation over the lifetime of PFI contracts.
He said the contracts "do reflect good value for money for the taxpayer" and "make sure that schools are getting value for money when it comes to cleaning, catering and everything else".
You can hear more about this story on Monday at 8pm in The Great PFI Debt on BBC Radio 4, and on BBC Sounds.
Are you affected by the issues raised in this story? Share your experiences by emailing firstname.lastname@example.org.
Please include a contact number if you are willing to speak to a BBC journalist. You can also get in touch in the following ways:
WhatsApp: +44 7756 165803
If you are reading this page and can't see the form you will need to visit the mobile version of the BBC website to submit your question or comment or you can email us at HaveYourSay@bbc.co.uk. Please include your name, age and location with any submission.