At first glance, William Richardson ticks all the boxes a new general secretary of the Headmasters’ and Headmistresses’ Conference should be ticking.

Privately educated? Tick. Extra points for his alma mater being an HMC signatory, Highgate School in north London. His university education includes periods at Russell group member Bristol University and New College Oxford, where he completed his doctorate. More ticks.

So far, so good. It is an academic CV that might have those caught up in the dogma of “maintained school good, independent school bad” rolling their eyes and muttering about elitism.

But hang on: the HMC’s new man sends his 15-year-old son to his local comprehensive - ahead of two local HMC schools. Why? Because it is good - and for him and his American wife, the school fitted the bill. He certainly wasn’t strong-armed into it.

And he does not even classify himself as an educationalist. He is, he says, more of a social scientist. He calls post-war state education an “unmitigated success” because it has broken down a host of social boundaries whereby people are no longer slotted into a career mapped out for them at birth, as was historically the case.

“It was a hierarchical society. There were limited situations that you could reasonably aspire to,” he says. “Prospects are much wider now than in the 1970s, which in turn were much wider than the 1940s. Children are now being prepared for a range of sectors they might take, whereas before they were being allocated a role.”

His praise for the country’s maintained sector might surprise some, given his position. It was, he adds, the profound changes to labour in the 1970s - the idea of a guaranteed job, he says, disappeared between 1973 and 1976, that forced schools to adapt.

“If you think about what society has become, it’s remarkable how much has been achieved through schools,” he adds.

The 55-year-old admits his new post is his last big job in a career that began as a “fast stream” management trainee at Unilever in 1982 and for the past 11 years has seen him based at Exeter University as professor of education, recently as head of the school.

Unsurprisingly, he is sensitive to the idea that he is too much of an academic to lead an organisation like the HMC. “It’s a fantastic job,” he says of his new post, which he officially took up at the beginning of September. “It’s not some academic capacity. The job is to promote and defend these schools.”

There is no mistaking he wants to move on the debate around state schools and independents - which too often gets mired in the language of class warfare - to something more sophisticated. In fact, this is the big story in town just now, with the prime minister and his education secretary pressing the top public schools into sponsoring maintained primaries and secondaries. Indeed, one of his earliest duties in his role was to attend a Downing Street summit on the subject hosted by David Cameron himself.

He is, however, enigmatic on the subject. “There is no point in starting (the process) if it’s not of mutual benefit. Academies are one of the recognised models of working with maintained schools, but HMC doesn’t endorse it as the primary method,” he says.

“We don’t have a model that we have prioritised for schools to follow. There isn’t a sense that this is anything other than an appeal to get involved with this Coalition policy. It’s only an appeal and can’t be a requirement.”

Dr Richardson also wants to make these kinds of debates more “data-led”, he says. And like an incoming general secretary of the HMC should, he has a strong grasp of facts and figures.

Citing a Mori poll carried out three years ago, he insists the proportion of parents who would send their children to independents “if they could afford it” rose from 51 per cent to 57 per cent between 1997 and 2008; more tellingly, the poll found the number of Labour voters admitting they would send their children to independents went up by a third to 54 per cent between 2004 and 2008.

He also quotes figures from the Independent Schools Council, which found that 40 per cent of pupils at UK independents in 2006 had parents who never went to a fee-paying school.

It is a rosy set of stats, boosted by HMC’s own figures which show that pupil numbers at its schools inched up by a cumulative 2.5 per cent between 2006 and 2011 - all this in the teeth of a recession longer and deeper than those of the early 1990s and the one in the previous decade.

Dr Richardson thinks independents are far more in reach of parents now than ever before, and this despite the rocketing fees being charged by many top public schools. “There are more people who can afford big-ticket items because of the consumerism society. There is more disposable income for a day school now. These schools are full and turning people away. There’s no sense these fees cannot be levied.”

Fees are simply about supply and demand, he says. To most, the kind of annual fees Winchester College, say, is now charging - at #163;31,350 they are nearly #163;6,000 more than the UK national average salary of #163;25,900 - are eye-wateringly high, but “boarding schools that charge the highest fees feed a group in society that for them is highly affordable”, he says.

Dr Richardson’s comments about consumerism are interesting, given that he is speaking in the wake of the riots that scarred London, Birmingham and Manchester.

“In some communities the return of a Conservative government has somehow managed to disenfranchise young people. (But) it’s more complicated than that. Nobody knows the impact of the imagery of consumerism. It’s very complicated.”

His willingness to talk about such issues suggests a man who will not allow the HMC to become isolationist. Indeed, he has already been meeting his members and is not troubled in the way others have been that somehow standards will be reduced as a sop to social mobility. Bursaries and reduced fees have expanded, he says, which has helped to boost total pupil numbers at HMC schools to just over 198,500. “Knowing these heads, there is absolutely no possibility of dumbing down. They are passionate about the quality of education,” he says.

The commitment to standards is what makes parents - whether well-off or not - stump up fees, he argues. “Independents are a pretty constant premium product. They’re quite secure and predictable in their outcome and that must be attractive to people.”

His immediate in-tray is likely to be weighed down in the coming months by work relating to the relationship between universities and his member schools.

In June, schools minister Nick Gibb said the top 10 universities were drawing 40 per cent of their intake on strategically important courses such as engineering, science, maths and languages from private schools. But HMC’s new incumbent does not seem as worried as his predecessor, Geoff Lucas, who recently voiced the view that some HMC schools are privately concerned that their pupils will be overlooked in favour of children from the state sector with similar grades.

“We’re not noticing anything like that,” he says. “Academic staff at universities want to teach the most able applicants who apply, regardless of their background.”

But he admits schools are targeting university places more carefully to copper-bottom the application process for their pupils.

“Britain’s higher education is about to be reformed very quickly,” he says, with an eye on the tuition fees being levied from next year. “Like secondary schools, we have to understand the importance of the changes in higher education. It’s such a rapid change, and at the moment we don’t know how it’s going to pan out.”

Dr Richardson’s role is to ensure that he maintains the kind of numbers which see 60 per cent of all independent school pupils who progress to university coming from an HMC school. This is no small undertaking - but it’s clearly one he believes in.

DR RICHARDSON CV

William Richardson completed his doctorate in Tudor religious history at New College after three years studying theology and religious studies at Bristol University. Before moving up to Oxford, he joined Unilever in 1982 as a management trainee, specialising in industrial relations, then took a research fellowship at Warwick University centred on education and industry. In 1995 he moved to Sheffield University, where he was a lecturer in the history of education. He moved to Exeter University in 2000 and two years later became the head of the school of education.