With days left to the close of the DfE’s consultation “Schools That Work For Everyone”, we can expect continuing arguments about the role of grammars, independent and faith schools and universities.

Do they have a role in creating the thousands of new places in good schools for children from lower income families? Or are they a side show?

Either way, you might expect those of us who lead independent schools to want this consultation to go away and the government to leave us to get on with the day job.

Not so.

We may not be the most popular kids in the class, but, a bit like the school swot, we think we have some answers.

Not to the whole big question of how to improve the state school system - that’s for our state school colleagues and government to decide.

But to the question of how to create thousands of new places in good schools around the country -  and do so whilst continuing great partnerships with state schools covering specialist teaching, co-curricular and university admissions.

Today we are announcing those proposals and challenging the government to run with them.

Mmm. Not sure you have anything much to offer the state sector.  What’s the idea?

Heads, governors and bursars within the Independent Schools Council are proposing to create a large number of new, free places in our primary and secondary schools for children from lower income families; those on free school meals (FSM) and the “just about managing”.

Parents will pay nothing. The taxpayer will pay nothing extra for these places either, as the government would pay the normal cost for a state school place and the schools would make up the difference.

We estimate that in time, we might be able to provide up to 10,000 new places in our schools every year.

Whilst none of us are suggesting the only good places are found in independent schools, there’s no doubt that this could offer a life changing opportunity for many more pupils whose parents couldn’t afford fees.

It would also save the government around £250m on the capital cost of building new schools for the equivalent number of pupils, freeing up badly needed funds. This proposal has high impact, high value and low risk.

Oh come on, why would your schools want to do this? What’s the catch?

No catch. Contrary to popular belief, those of us who lead independent schools have the same devotion to developing children and young people as our colleagues in state schools.

Every one of us wants more young people to receive a great education and be exposed to the widest array of opportunities.

It’s in all our interests that  young people are well educated and able to contribute positively to society according to their ability.

One of the myths about our schools is that they are bastions of unearned privilege. The truth is that our schools are not-for profit charities, and just the 282 schools in Headmasters’ and Headmistresses’ Conference (HMC) spend over half a million pounds a day on means-tested bursaries and over a third of our pupils get help with fees.

And we want to find a way of growing that without having to raise money by putting up fees for our already hard-pressed parents and supporters. This proposal is a once in a generation opportunity to take a substantial step in extending those opportunities more widely.

The schools I represent are amongst the most successful in the world. If they were a country their results would be up with the top countries in the Pisa tables. They are a huge national asset; educationally, economically and socially. They have global reach and are recognised for their excellence not least by the government.

Why would you deny a child the opportunity of a place at such a school?

But what about helping provide good school places in state schools? Isn’t that more important than sending more children to posh private schools?

There’re both important which is why our multiple proposals to the government include developing the existing, long-standing, mutually beneficial partnerships with our colleagues in state schools (there are over 1,500) and working in consortia with state school partners to set up new schools across England.

In other words, we are challenging the government to support us in sharing our specific expertise where and with whom it is welcomed.

Do you really think the government will go for it?

That’s for Number 10 to decide. Some state funding of independent schools is not a new idea. It’s happening now; the specialist music and dance schools across England already receive funding from the state.

This could save the taxpayer millions and would mean a considerable contribution from independent schools who already save the taxpayer £3 billion a year from students not being in state education and contribute £9.5 billion to overall UK GDP.

Given that most independent schools are non-selective or not highly selective, the proposal would provide a stream of good places for children only on the basis of need and not by prior academic attainment.

OK. But why can’t you do more?

What we cannot offer is to change the education landscape for all children. We wish we could but the reality is that there are ten state schools for every one independent school in England and we educate roughly 7 per cent of pupils in schools with an average of just over 400 children.

Some are much smaller than that and only 70 have more than 1,000 pupils. We currently work with 10,000 state schools and 160,000 state-school pupils.

We are offering to add to this existing, extensive array of long-standing, mutually beneficial partnerships where there are willing partners.

But there is a limit to what we can do without putting at risk the excellence of our schools on which all this activity depends.

Mike Buchanan is headteacher of Ashford School in Kent and chair of the Headmasters’ and Headmistresses’ Conference (HMC). He tweets at @Ashfordhead

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