Ofsted! The Musical, the all-singing, all-dancing portrait of the joys of government inspection, has become one of the surprise successes of the Edinburgh festival fringe.

The show originally met with polite bewilderment when it appeared in the fringe programme. But, less than a week into the festival, it has been playing to night after night of sell-out crowds, an unprecedented success for the 89-seat venue.

David Byrne, its writer and director, said: “We’re all completely overwhelmed. We’ve been stealing ‘sold-out’ signs, so we can pin them up at home.”

Many of those queuing for tickets are teachers, eager to watch their stage counterparts triumph in song. Angela Lowry, from Heathlands primary, in Birmingham, said: “Ofsted isn’t the obvious choice for a musical. But this play makes something that is quite scary in real life seem almost enjoyable.”

Pippa Donati, who teaches English at East Berkshire college, said: “I came because I knew it would be a satire, and it’s good to laugh at the things that scare you.”

The musical’s plot is deliberately over-the-top, with a militaristic inspector proclaiming: “Schools are no longer filled with fear. I’m here to put it back.” And the Hull University actors knowingly overplay the anarchy of day-to-day school life.

But, says Sarah Turley, a primary teacher from Blackpool, it is surprisingly accurate. “They may be a stereotype: but it’s true they are militaristic. I hope inspectors come and see it.”

According to Mr Byrne, several inspectors have already attended. One, he said, laughed out loud when inspection stress led the play’s headteacher to suffer a heart attack.

But David Bell, chief inspector, is undeterred by such tales. He has launched a competition among inspectors for the best Ofsted report on the musical. “Unfortunately I can’t get to Edinburgh myself,” he said. “But I’m sure there will be lots of inspectors in the audience, and I look forward to reading the reviews.”