"GCSEs are possibly the worst thing ever invented and the Common Entrance Exam is the second worst thing.

"I would love to see children able to go through school without having to confront this kind of final exam culture which stifles creativity."

John Baugh is normally a very considered speaker, softly-spoken and painstakingly diplomatic.

That is until you get him onto the subject of exams.

"In 20 years' time I would love to come back and find the world has a better way of assessing whether children should be passing up to the senior school of their choice."

The reason Mr Baugh is talking of 'coming back' is that this term, after 15 years as headteacher, he is leaving the Dragon.

Nestled in a corner of Bardwell Road in what a national journalist once called 'leafiest north Oxford', the Dragon School has long held an enviable reputation for fostering enormous talent: Hugh Laurie, John Betjeman, Emma Watson, Tim Henman, Tom Hollander – the list of superstar alumni goes on.

So what is the Dragon's secret, and just what part has John Baugh played in it?

The school has deep roots in progressive educational theory.

Founded in 1877 by a group of Oxford University dons for their own children, it today describes its ethos as 'a dynamic balance of relaxed unpretentiousness and academic discipline which has been described as robust informality and relaxed rigour'.

The actor Tom Hiddleston recently told an interviewer: "I don’t remember 'learning' anything, and yet I learned everything."

There's a funny parallel to that quote when John Baugh is recalling his own earliest school days in Uganda (his father was in the British Colonial Police): "I don't remember anything about lessons, I just remember running around with the chickens."

It was not long after that, aged 15 and then going to Aldenham School in Hertfordshire, that he first wanted to be a teacher.

He recalls: "I had one or two teachers who I really admired the way they dedicated their lives to what they were doing.

"I wanted to do something with value."

He has now been doing something with value for some 40 years – 31 of those as a head at various schools.

Yet despite his enviable CV, it is remarkably hard to draw out of him any driving single ambition or personal mission.

"I never analysed what worked for me... I just remember learning most and feeling safest at schools when I knew I had good relationships with my peers and teachers, where there wasn't that command-and-control dogma – where it was about building relationships."

It gets better: when asked how that relationship works in practice at the Dragon, combining the seemingly contradictory ambitions of pupil-teacher friendships and enforcing rules to make sure everyone is safe and happy, the 61-year-old explains the 'covenant' where children are asked what sort of environment they would like to live and work in, a set of guidelines which they are then expected to stick by.

If it sounds fluffy – and Mr Baugh happily admits 'we've always strived to be just slightly off-centre' – the proof is surely in the pudding.

And if Mr Baugh has not steered the Dragon in radical new directions during his time there, it may be because he was an almost perfect fit for the school's long-established progressive philosophy, for which parents fork out up to £28,000 each year.

Asked for his great achievements over a decade-and-a-half, he ponders for a very long time before slowly and cautiously replying: "I generally think the school is a more thoughtful and compassionate place than it was," quickly adding: "Without implying this wasn't a lovely place when I arrived."

The veteran educationalist is departing the world of full-time work to embark on what he reluctantly admits is best described as 'consultancy': the 21st century pot of gold that awaits the most successful and distinguished in their field.

He talks of international work and maybe even going back to East Africa.

Then, of course, there is that niggling unfinished business: Mr Baugh's long-held foe, the standardised exam system.

When he talks about the 'unavoidable' pressure it puts on teachers and pupils, there is no fluffiness about him.

And, given the how far so many illustrious dragons have spread their wings, maybe we should not find the idea as outlandish as it first appears.

"That would be a wonderful gift to the children and the teachers: meaning they could get on with really being creative and stretching their minds which we try to do as much as possible."