By contrast, plans for another academy at nearby Conisbrough, also sponsored by evangelical Christian Sir Peter Vardy, were shelved last month after parents' protests.
Ian Brew, the Trinity head, said: "I have had people asking if we are going to ram religion down children's throats, or make them carry bibles everywhere," he said.
But Mr Brew, a creationist, said these were misconceptions. By speaking "honestly and openly" with parents, they had won them round. The prospect of a brand new building and the school's belief in uniform had also helped.
Jane Clamp, whose daughters Emily and Jessica start at the school next September, said: "I think what gave me confidence was their confidence that they could do a better job. It was the results it achieved rather than the school's academy status that were most important, she said. "City academy is just a title, really."