Once again, private schools will dominate the UK’s exam results this summer - at GCSE, A level, Pre-U and in the International Baccalaureate. We make up 15 per cent of those taking A levels but gain a third of the top grades. Independent schools perform especially well in the harder subjects, gaining half the top grades in A-level modern languages and more than a third of the top grades in the hard sciences.

Because independent school students do so well in the subjects that the better universities are looking for, they gain a large proportion of the places available at those universities. Many university modern languages departments would be forced to close if our students were not there, filling the gap left by the collapse of languages teaching in maintained schools. Numerous top medicine, engineering, mathematics, Classics and music departments depend for their viability on our students.

And when they reach university, our students do better than those from the maintained sector. In July, the Higher Education Funding Council for England published an analysis of the degree results of the 226,000 UK students who started their degrees in 2006: 64.9 per cent of those who had come from independent schools gained a first or upper second, compared with 52.7 per cent of students from state schools.

Independent schools are also propping up sport in this country. More than a third of medal winners at the 2012 Olympic Games came from our schools, as did 30 per cent of county cricketers and the majority of the England cricket team, even though our schools educate only 7 per cent of pupils.

The Office for Fair Access requires universities to set “access targets”, a concession made to the Liberal Democrats in return for their support of higher tuition fees. Many universities have been persuaded by the Higher Education Statistics Agency to target a reduction in the proportion of students coming from private schools. University College London, for example, is aiming to decrease the proportion of students from private schools (currently 35 per cent) by a further 10 per cent by 2017.

One reason that this is so wrong is that private schools now educate large numbers of bright students from lower-income backgrounds. More than a third of our students are on reduced fees, and many receive means-tested bursaries aimed at children from the lowest-income homes. When I started teaching 40 years ago, bursaries were unheard of and most scholarships went to children from wealthy homes. Today, much of that money has been diverted to means-tested bursaries.

This is why the University of Oxford refuses to use privatestate school ratios in its access targets because, as its latest access agreement says: “There are students from relatively wealthy backgrounds at state schools, and students from relatively disadvantaged ones at independent schools. Thirty per cent of 2012 entrants in receipt of the full Oxford Bursary (students with a household income of #163;16,000 or less) were educated in the independent sector.”

Another reason why the emphasis on independentstate school targets is so wrong is that it permits universities to claim they are doing their bit for social mobility when in fact they are simply taking more students from selective grammar schools and middle-class comprehensives. The measure fails to identify the most disadvantaged children, in the most deprived areas, which is where the battle for improved social mobility really needs to be fought.

Why parents push to find the fees

The majority of parents who send their children to independent schools find the fees a struggle (the average fee for day schools is #163;12,000 a year). I know many parents who are taking short holidays in the UK this summer in order that they may pay next term’s fees. But they do so because private schools produce results. They achieve the best academic results, their students go to the top universities, they have good pastoral care and they are outstanding at sport and the arts.

Since 1997, the number of private schools working with state schools has grown to the point where almost all private schools are involved in one project or another. I am chair of governors of the London Academy of Excellence in Newham, East London, which provides top-class A-level tuition (hard subjects only) in a borough with a shortage of A-level places. Our free school is supported by staff from institutions such as Brighton College, Eton College, Highgate School and Roedean School - all good private schools. Several thriving private schools sponsor academies; many more, such as Radley College, work closely with a partner state school to raise standards. This is not window dressing: these schools are devoting a great deal of time and resources to improving their partner schools and, in doing so, are helping to transform education for all children.

We receive no reciprocal support from the state. Unlike so many of the highest-performing countries, including Australia, Finland and Hong Kong, whose governments provide funds to help private schools, we receive no direct financial assistance. For those schools with charitable status, the tax benefits are modest. We run our schools efficiently and make small or no surplus on the income. This is why we have to charge the fees we do and lack the capacity to expand further in the UK.

Independent schools receive regular requests from foreign businesses and governments to set up branches abroad. More than 1.4 million students study in the 3,000 British schools overseas (where at least half the curriculum is British). Private schools in Britain now run 30 overseas branches with 20,000 students - a figure that will soon overtake the 26,000 international students studying in our schools in the UK. So, like the universities, we are part of an international network. Facing obstacles to growth in the UK, we have looked overseas.

In his 2012 Reith Lectures, economic historian Professor Niall Ferguson said: “In my opinion, the best institutions in the British Isles today are the independent schools.” But at a time when some private schools have unfilled places, state schools are buying up Portakabins to cope with shortage of space. As a country, are we making best use of this national asset?

Barnaby Lenon is chair of the Independent Schools Council.