‘Poor and indigent scholars.” Time and again that is the phrase embedded in the founding ideals of England’s great public schools. Harrow was established as a grammar school “by instinct of charity” to educate the neediest. Dulwich College was set up by the impresario Edward Alleyn for “poor scholars” from London’s toughest boroughs. But now, according to Andrew Halls, head of King’s College School Wimbledon, these centres of learning are little more than “finishing schools for the children of oligarchs”.

Created in a culture of philanthropy and Christian duty, too many independent schools have become barriers to British educational success. The division between state and private education damages our society, stifles opportunity and, by wasting talent, inflicts damage upon our economy. If we are to prosper as a country, we need to be more equal. Some private schools want to overcome this corrosive divide of privilege, but most do not. It is time to stop asking politely.

There is unfinished business in this. “The public schools are saved,” reflected Rab Butler, 70 years ago, of his 1944 Education Act, “and must now be made to do their bit.” Ever since then we have been wrestling with just what “their bit” entails. It defeated even Anthony Crosland as education minister. “Now what are we going to do about those damned public schools?” he asked a group of heads in 1965. Before opting for the depressingly obvious. “I suppose we must have a royal commission, something like that.”

Labour has acted most effectively in bridging the public-private divide. When last in government, we scrapped the assisted place scheme to fund smaller infant class sizes, nationalised a number of private schools and urged the Charity Commission to take a much closer look at the public benefit activities of private schools. Thanks to opposition from the Independent Schools Council (ISC), that strategy collapsed in the law courts and since then the Tories have done nothing to breach this Berlin Wall in our education system.

In the wise words of the upper tribunal, adjudicating between the ISC and the Charity Commission, “these are issues which require political resolution”. Although private schools, including the one that I went to, educate only 7% of children, their students take up almost 50% of Oxbridge places. Analysis by the Sutton Trust reveals an interesting spectrum: an independent day school student is 22 times more likely to attend a Russell Group university than a state school student from a disadvantaged background.

I believe we deserve an education system where the majority of young people enjoy the same access to excellence as the privileged 7%. With ever growing concentrations of prosperity and power, we need a system that challenges all institutions to work together to spread social mobility. And at the moment that is not the case: only 3% of private schools sponsor an academy; only 5% lend teaching staff to state schools. According to the chief inspector of schools, Sir Michael Wilshaw, this model of partnership between independent and state schools is meagre stuff – “crumbs off your table”. And so, rather than expending energy on educating global elites in Shanghai and Abu Dhabi, England’s public schools should start to rediscover their original, charitable ethos.

However, it needs to work both ways. Those working in the state sector could do more to acknowledge that for all the advantages of selection and wealth that private schools enjoy, they also contain world-beating educational attributes. In subject knowledge, pupil confidence, co-curricular activity, and staff development, independent schools have lessons for the state sector. In turn, private schools have a great deal to learn from mainstream schooling on whole-class teaching, modern British values, student engagement and, indeed, value for money. This has to be a relationship of respectful, advantageous interaction.

So Labour’s plan is this: we will introduce a School Partnership Standard requiring all private schools to form genuine and accountable partnerships with state schools if they want to keep their business rates relief. We will encourage each institution to reflect on the skills, traditions and educational needs of their locality, and then develop an action plan to deliver tangible reform.

We want to see more private schools running summer schools, sponsoring academies, assisting state boarding schools and assisting professional exchange. In fact, just the kind of public-private partnership already taking place at the United Learning Trust, with its mix of 38 academies and 13 independent schools successfully sharing cultural and sporting experiences, developing clusters to improve university access and supporting teacher development.

But we will also bring to an end the charade of those schools who think a spurious bursary scheme, hanging up some artwork or allowing access to gardens fulfils their social responsibility. It doesn’t. With a Labour government, private schools will only be exempt from business rates if they can show a meaningful impact on state education.

England’s independent schools need to raise their game. Britain will only thrive in the 21st century on the back of an education system where pupils enjoy equality of opportunity. This crippling public-private impasse has gone on too long. Ed Miliband’s Labour party is going to end it.