Britain’s most expensive state school is being built without a playground because those running it believe that pupils should be treated like company employees and do not need unstructured play time.

The authorities at the £46.4m Thomas Deacon city academy in Peterborough, Cambridgeshire, due to open this autumn, also believe that the absence of a playground will avoid the risk of “uncontrollable” numbers of children running around in breaks at the 2,200-pupil school.

“We are not intending to have any play time,” said Alan McMurdo, the head teacher. “Pupils won’t need to let off steam because they will not be bored.”

The absence of play time has angered some parents whose children will attend the school, designed by Lord Foster, architect of the “gherkin” office tower in London. But staff insist that it will have the added benefit of avoiding pupils falling victim to playground bullies.

Miles Delap, project manager at the academy, said: “For a school of this size, a playground would have had to be huge. That would have been almost uncontrollable. We have taken away an uncontrollable space to prevent bullying and truancy.”

Anne Kerrison, who has three children, said her 14-year-old son Matthew was devastated when he discovered that he would not be able to kick a football around at lunchtime.

“All children need fresh air and a chance to exercise during the school day. Break times are the only unstructured time they get,” she said.

Another city academy, Unity in Middlesbrough, opened in 2002 without a playground, prompting criticism from government inspectors about poor design. The school later built a playground.

Thomas Deacon, nicknamed “the blancmange” because of its rounded shape, will be one of the biggest schools in Europe. Its features will include a “wetland eco-pool” designed “for rain-water collection” planted with wild flowers. It will replace three schools in Peterborough and is one of the showcases of Tony Blair’s academies programme.

Academy schools remain in the state sector but are independent of local councils. They are sponsored by private sector firms which have some say in the management.

The academy’s timetable will be tightly structured and exercise for pupils will take place in PE classes and organised games on adjacent playing fields. There will be a 30-minute lunch period when pupils will be taken to the dining room by their teacher, ensuring they do not sneak away to run around.

McMurdo said refreshments, often taken in break periods at other schools, could be drunk during the school day. “[Pupils] will be able to hydrate during the learning experience,” he said.

Other head teachers questioned the wisdom of the playground ban. Ian Andain, head at a comprehensive in Liverpool, said: “There has to be bit of open space to play football. It is important that pupils can have a run around and expend energy.”

However, Delap, who has run the academy project on behalf of its sponsor, Perkins Engines, and the Deacon school trust, said that playgrounds did not fit into the concept.

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