Two private schools that were considering becoming academies have ruled out the idea.
Salisbury and Lichfield Cathedral Schools were two of several schools that had thought about becoming academies in the state sector as the credit crunch begins to bite for fee-paying schools.
It was announced last month that two prep schools, Bramcote Lorne in Retford, Nottinghamshire, and Brigg in Hull, were being forced to shut at the end of term.
High-profile MP Frank Field has previously urged private schools to consider the academy switch.
But Salisbury, an independent choir school with 200 mixed pupils aged 3-13, decided that it was not suited to becoming an academy because it is too small and its intake is too young.
Lichfield, which takes children aged 3-15, is widening its age range to become a full secondary school with a sixth form.
While both had considered following the lead of Belvedere School in Liverpool, which became an academy two years ago, they have now decided against.
Bristol was the first choir school to become an academy, making the switch in September.
But Peter Allwood, Lichfield's head, said: "Because we are going through such an expansion, it's not a time to bring other changes in and we value our independence."
He said the school had been interested in becoming an academy because it wanted to attract children from a wider range of backgrounds. But it had decided to continue to do this through outreach work, schemes with state schools and scholarships.
Mr Allwod said that while some private schools might consider becoming an academy because they were struggling to attract fee-paying pupils, this was not why Lichfield had considered the move.
Salisbury's chair of governors, the Very Reverend June Osborne, said cathedrals often found it hard to fund enough scholarships and bursaries for pupils whose parents could not afford full fees.
"We have no difficulty filling the school, but there is an issue that nobody wants to make the salaries of the parents the dividing line between those who can access this kind of education and those who can't," she said.
Academy status appealed to the school because it would enable it to maintain its independence and ethos while opening its doors to a wider group of pupils, she said.
She said Mr Field, who chairs the Cathedrals Fabric Commission for England, had encouraged all cathedral schools to consider the possibility of becoming academies.
Belvedere Academy, pages 18-20.