A school which cost £18.6 million to rebuild six years ago needs to spend £5 million on repairs - including fixing some 300 holes in its roof.
Wolverhampton Council leader Cllr Roger Lawrence said he feared the school has been the victim of ‘corner cutting’ by builders.
King’s Church of England Secondary School in Tettenhall was rebuilt by the construction giant Carillion in 2012.
But when the company went into liquidation in January this year, it left the bill for the repairs with the Church of England diocese.
It is now hoped the Department of Education will provide extra funding for the voluntary aided school that is directly funded by central government.
Funding shortages have added to the school's problems as 14 staff have been cut to cope with a £350,000 cut in funding.
Despite the difficulties it faces, it was been described as the most improved school in Wolverhampton in 2017.
James Ludlow, the school's head, describing the situation said: “It's really heartbreaking.
"When it rains, and we've had some heavy downpours, water comes through into the corridors and brings bits of the ceiling down."
The school has had to stop subsidies to children from poor families for music lessons and cancelled its annual play.
Cllr Roger Lawrence has now told councillors the authority will help the school overcome its problems with repairs.
Explaining that the building and land is owned by the Lichfield Diocese and not the responsibility of the council, he said the authority had commissioned a consultant's report on the work that needed to be done.
At the authority's full council meeting he said that he feared Carillion had ‘cut corners’ during construction.
“We have engaged in a much more productive dialogue with the diocese and the school over the last few months,” he told councillors.
“Schools are absolutely crucial to the future of our city and the quality of education to a degree depends on the quality of the buildings available and it appears here that there are outstanding issues that need to be addressed.”
