The Telegraph says that an 'elite group of schools' including flagship academies and state grammar schools have received more than 1,000 applications each for this September.
With almost 600,000 children across England receiving news of their secondary school place today, it is claimed that demand for the most sought-after schools is on the rise as more parents remove children from private education because of rising costs.
Demand is said to be 'more intense' in cities such as London where parents can choose between dozens of senior schools and selective grammars – resulting in as many as half of those children missing out on their first choice school.
The Telegraph says the situation is likely to lead to 'thousands of parents lodging official appeals against school placements'. The paper quotes Graham Jones, a former head teacher and founder of School Select - an organisation which helps families through the school's appeals process - as saying the best schools were reporting a 10 per cent rise in applications.
"There have been year-on-year increases in appeal enquiries and this year it is expected to rise again," said Mr Jones.
One example cited was the West London Free School in Hammersmith which had 1,178 applications for just 120 places.
A Department for Education spokesman said that 'every parent should have the choice of a good school for their child' and claimed they were 'turning around' under-performing schools by allowing outstanding sponsors to lead them. They also said they were 'allowing good schools to expand and offer more places'.
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