St Luke’s science and sports college had to close its doors last Friday to allow for emergency fumigation after the flea outbreak was discovered and some pupils demonstrated for the right to be sent home.

The college has also had to close its sports pitch after stones came to the surface, risking injury to pupils. The same problem is affecting St Peter’s school, which has also had to rule its new pitch out of bounds.

And Isca college of media arts was forced to deep-clean parts of its new building last month after a mystery smell led to staff and pupils saying it was making them sick.

The schools were all built as part of a multi-million pound regeneration programme to coincide with the abolition of Exeter’s middle schools.

Five new secondaries have been built under the private finance initiative, but the project has been beset by delays.

The original PFI contractor, Mowlem, was taken over by another company, Carillion, and the schools moved into their new buildings up to nine months late.

St Peter’s was due to move in January last year, but had to wait until September. It has been in dispute with Carillion about the state of its sports pitches since.

Staff from Carillion have visited St Peter’s and St Luke’s this week to seek ways to fix the pitches.

Nine hundred pupils were given the day off at St Luke’s last Friday while the school was fumigated.

Dave Clinch, secretary of Devon NUT, said: “Since the PFI schools opened there has been a catalogue of incidents, which has led to disruption to teaching and learning.”

The problems renew concerns about the ability of the PFI model to deliver high-quality schools. The initiative will be widely used over the next 15 years to refurbish all secondary schools.

A spokeswoman for Carillion said: “The flea issue was not in our control.

The smell at Isca has now been eradicated. As for the pitches, we have brought in independent experts to see what can be done to resolve the problem.”