It takes some serious self-confidence to say no to the prime minister. It is with this in mind that independent school heads will be considering a letter recently sent by David Cameron that further cranked up the pressure for them to forge closer links with the maintained sector.

Extracts of the note to William Richardson, general secretary of the Headmasters’ and Headmistresses’ Conference (HMC), seen by TES, include the prime minister telling heads of the HMC that such schools “have a duty” to sponsor academies.

The Eton-educated prime minister has put the issue at the heart of the Government’s plans for state education and wants his former school and others, such as Harrow and Rugby, to sponsor academies.

“HMC schools offer an outstanding, truly world-class education,” Mr Cameron said in his letter to Mr Richardson. “I believe that they not only have a duty to share this expertise by sponsoring academies but that they will also gain immeasurably from the experience of doing so.”

The note comes three months after Mr Cameron called in 10 leading independent heads to a Downing Street summit in which he put heavy pressure on the schools to get involved. It was also attended by Michael Gove and former Labour schools minister Lord Adonis.

“I recognise the value of bursaries and the importance of existing partnerships,” the prime minister added in his letter. “But we are looking for something more organic, more lasting and profound.”

He told Dr Richardson, who took up his post in September, that he hoped “you will feel able to encourage HMC schools to follow the academy path” and that HMC schools would be “able to respond positively to this request”.

A number of independents are already pushing on with plans to take over struggling primary schools, with a dozen leading schools - including City of London Boys’ School and Dulwich College - actively looking at the idea. Last week, TES revealed that Manchester Grammar is hoping to set up a free school in a run-down part of the city in 2013.

And in an interview, due to be published in TES this month, Harrow headmaster Jim Hawkins stated: “We’ve got to look at the education system nationally and learn from each other. Where there is best practice in either, we have to transfer that across.”

But the reception for the prime minister’s pet initiative has been lukewarm at best in many quarters of the independent sector.

“It is only right for us to be involved in partnerships with other schools, but it is not right for us to be told how to do so,” warned the president of the Girls’ Schools Association, Helen Wright, last month. “Why should our parents - most of whom struggle hard to pay the fees to educate their children - prop up the state system and so effectively pay twice?”

Dr Richardson denied HMC schools were being forced to bow to Government demands. “It’s a Government policy and they want all supporters on board. Our meeting with the prime minister was one of a number of meetings with interested groups.”

He said the group is having continuing discussions with schools commissioner Elizabeth Sidwell, but had not been given a timetable to fulfil Government wishes. “HMC schools are embracing academies where the trustees concerned have deemed this to be a “best fit” form of partnership. We will work with Liz Sidwell to enable others to embark down the same road.”

CASH QUIBBLE

The chief executive of the Independent Association of Prep Schools has said the Government should stop wasting money on building free schools and hand the cash to parents to allow them to send their children to independents instead.

“Common consensus is that it costs #163;6,000 a year to educate a child of primary age in the state sector,” said David Hanson, a former director at academies chain United Learning Trust, who also attended the Downing Street summit. “They should allow parents to take that #163;6,000 a year and be able to add to it by whatever amount they wish.

“Instead of wasting #163;600 million on building new (free) schools, what we should be doing is giving all parents the true freedom of choice.”

Mr Hanson said that giving money to children’s parents was no different from pupils being asked to pay thousands of pounds for their degree courses.