“Middle classes abandon state schools” was the front page headline of The Daily Telegraph.

A slight exaggeration, perhaps, given that their figures showed a rise of just 0.2 per cent - from 7.1 to 7.3 per cent - in numbers attending independent secondary schools over the past three years.

But while abandonment might be an overstatement, it does fit in with a longer-term movement from the state to the private sector.

Figures covering all types of schools show that the market share for the independent sector has risen from 7.3 to 7.7 per cent over the past 10 years.

The increase is explained in part by a drop in the birth rate during the 1990s. The dip mainly affected poorer families who could not afford private schools, while better-off families continued having children and sending them to fee-paying schools.

The raw figures show that attendance at independent schools has actually fallen slightly over the past five years, although it is up by around 20,000 over the past decade.

Sam Freedman, director of education research at the think-tank Policy Exchange, said: “Over time, there has been a gradual increase in the number of children in independent schools. Every year there is an abandonment story, but it’s never that severe. It’s a drip-drip effect.”

The increase comes despite rapid rises in independent school fees, which have increased by around 40 per cent in the past five years.

In around a third of local authorities, more than 10 per cent of children are in private education.

Mr Freedman said that many of these authorities were in London, where areas of deprivation jostle with areas of wealth.

“That makes it difficult for state schools to attract well-off middle-class parents,” he said.

If demand were to increase rapidly for independent schools, the sector would struggle to accommodate many more children. Popular and over-subscribed schools find it difficult to increase their capacity.