The decision to close East Brighton college of media arts was taken last week. Despite being reopened under the Fresh Start scheme in 1999, the 450-pupil comprehensive stayed half-empty and last year only 12 per cent of pupils got five A*-C grades at GCSE.
Jarvis, which built and maintained the school under a private finance initiative, is seeking pound;4 million from the council to maintain the empty building.
A spokesman for Jarvis Accommodation said: "We were contracted to provide certain services. The council has a contractual obligation to us."
The much-criticised firm, which is under investigation over its role in the Potters Bar rail crash, is now bidding for educational contracts under the name Engenda.
Mark Whitby, executive principal of East Brighton, said: "The authority could put pound;4m into our school instead, but if we have no pupils it won't make a difference."
Pat Hawkes, chair of the schools committee, said the penalty will only apply if the site remains unused. She said: "If the school is mothballed, we will have to pay Jarvis. We're determined to use it effectively - then we can use the money for education and training."