Eight years ago, King David high school in Liverpool was looking for a new headteacher. With 12 years’ service at the school - as head of biology, deputy head and finally acting head - John Smartt seemed the right man for the job. The only problem was his religious faith.

King David is a leading Jewish secondary school, but Mr Smartt is a practising Roman Catholic. So the decision to appoint him was unusual, perhaps unique. But then King David high is an unusual school. Its mission statement is clear enough: “to preserve and develop a religious ethos in accordance with the principles of the orthodox Jewish religion”. But the reality is more complicated. Fewer than one in three of its 600 pupils are Jews and many of these come from a liberal, rather than orthodox, background.

Each year, the school is hugely oversubscribed. Priority is given to Jewish pupils, then to non-Jews from nearby King David primary school, while the remaining 30 or so places are contested by more than 200 applicants. So why do parents of all faiths - and sometimes of no faith at all - queue up to send their children to an orthodox Jewish school?

John Smartt cites King David’s academic success - a 95 per cent pass-rate at A-level - and its strong musical tradition. Parents are also attracted by an environment of clear morals and firm beliefs. “The fact that they don’t share those beliefs seems not to matter,” says Mr Smartt. Nor does it seem to matter that he doesn’t share those beliefs himself.

“The pupils and the parents are happy with it. People say the school has actually become more Jewish under my leadership. Perhaps as a non-Jewish head, I’m even more keen to uphold certain values because I know what people might say if I didn’t.

“We’re not a multi-faith school; we’re a single-faith school which accepts pupils from other faiths. Every teacher and pupil abides by certain Jewish principles here, regardless of how they live at home.”

However, not everything divides neatly into home and school life, and inevitably there are sometimes grey areas.

“If I attend a conference on a Saturday, I don’t advertise the fact that I’m from a Jewish school. If it comes out, I always make sure that everyone knows I’m not Jewish.”

The need to tread carefully can make life complicated. Decisions on “Jewish matters” are taken only after consultation with the school’s head of Jewish studies. Some heads might feel that having to “ask the expert” all the time could undermine their authority, but it’s not something that troubles John Smartt. “If I had an autocratic style of leadership, it would bother me. But I believe in sharing responsibility,” he says.

After 20 years at King David, his knowledge of Judaism is thorough, but he still makes mistakes. After a recent speech day address, a sixth-former pointed out an error in a scriptural reference. “He was worried about correcting his headteacher, but I applauded him. In this case, he had more authority.”

But in general, day-to-day practicalities pose more problems than theology. “There are things to remember which may be second nature to someone of Jewish culture, but which aren’t to me,” says Mr Smartt. Hence a recent panic when local authority workers almost extinguished the eternal lamp while doing some wiring repairs. At other times, the challenge is to make outsiders aware of the school’s customs and beliefs. Display boards show newspaper cuttings about the crisis in the Middle East. Year 8 pupils cook kosher pizza-bagels in their domestic science lessons. But there are still occasional threats to the school’s identity and culture.

“The DfES is always telling me I have spare places,” says Mr Smartt. “They don’t understand that we need extra space. Classes split so that Jewish pupils can learn Hebrew, while the others learn German. And we can’t teach PE in mixed-gender groups.”

He admits that he would not have applied to be the head at a Jewish school if he had not already been working in one, and believes that the governors wouldn’t have appointed a non-Jewish head they were unfamiliar with. “It’s a strange situation,” he says. “But it works.”

But aren’t such fundamental differences in belief a barrier to effective headship? Should a head not personify the school’s values?

“In one sense that’s true,” he says. “But at the heart of any faith school, there must be understanding and tolerance of other religions. That’s one area in which I can definitely lead by example. Being a non-Jewish headteacher makes me think about what faith is, what really matters.”