Her eldest daughter, Mollie, easily passed the entrance test to the town’s high-performing Pate’s grammar but only just squeaked in because a new co-ordinated admissions system, which is meant to be fairer, is denying real choice to thousands.

The problem for Ms White and her daughter was the decision by four good foundation schools in the area, which are responsible for their own admissions, to insist on a “first preference” system which means schools know if parents have ranked them first.

The family had moved into the catchment area of Balcarras school, a very popular, oversubscribed foundation comprehensive and technology college, on the eastern edge of the town.

But Ms White knew that if she ranked it second the chances of getting a place would be almost zero.

If she had known the result of the Pate’s entrance test the decision would have been simple - but she did not.

So she put Pate’s second. “I felt I couldn’t risk it. If she had failed the test she might have ended up being allocated the kind of school that would have got very few first preferences and we’d have been stuck.

“I’ve got a friend who put Pate’s first. Her son didn’t do well enough in the test and she is now wandering around still trying to find a place for him.

“I can’t afford private education to get us out of a situation like that.”

The numbers taking Pate’s entrance test dropped by around 250 to 550 yet the numbers of children from private schools who took the test stayed roughly the same at around 120.

The result is that number of children admitted this September who were previously privately educated will double.

Richard Kemp, the head-teacher of Pate’s is deeply disappointed. For the past four years he has collaborated with the Sutton Trust to provide weekly half-day sessions at Pate’s to stretch the brightest from a group of primaries in the most deprived pockets of the town.

“It is the bright children from the less advantaged areas that are most disadvantaged in this system - it’s a double whammy,” he said.