Favid Cameron said he is "terrified" by the prospect of sending his children to a state secondary school in central London.
The Prime Minister said he understood why some parents decided to "break the bank" to pay for a private education because of the low standards of many comprehensives. He will have to resolve his dilemma in five years' time when his eldest daughter, Nancy, finishes primary school.
Mr Cameron said the problem had strengthened his determination to pioneer a new generation of "free schools". He said: "There aren't enough good school places, that's the problem. And that's why we're trying to have more good schools. In some parts of the country, there isn't a choice of good schools. That's why people break the bank to send their children private."
Asked by the News of the World if he sympathised with parents who can't get their children into a high-quality school, he replied: "Totally. I've got a six-year-old and a four-year-old and I'm terrified living in central London.
"Am I going to find a good secondary school for my children? I feel it as a parent, let alone as a politician."
Mr Cameron, who was educated at Eton College, sends Nancy to a Church of England primary, St Mary Abbots in Kensington. He and his wife, Samantha, who is seven months pregnant, rejected 15 other state schools for Nancy before settling on the school two miles from their previous home before moving to Downing Street. Mr Cameron insisted last year he would send his children to state secondary schools – as long as their standards were high enough. "I think it's crazy that we should pay lots of money for private schools. We all pay our taxes. You should have really good state schools available for all," he said.
Tony Blair sent his sons, Euan and Nicky, to the grant-maintained London Oratory Roman Catholic school in Fulham, west London. Their sister Kathryn attended the Sacred Heart High School in Hammersmith.
Gordon Brown, while Prime Minister, sent his elder son, John to Millbank Primary, the nearest primary school but one to Downing Street. However, John and his three-year-old brother Fraser, who is at nursery, will be enrolled in Scottish schools next term.
Last night Westminster City Council, which covers Downing Street, said its schools provided "first-rate education every day". Nickie Aiken, Westminster's cabinet member for children and young people, said: "We are proud that several of our secondary schools are considered outstanding by Ofsted and that our nearest primary schools to Downing Street are also both rated outstanding.
"We acknowledge there is still room for improvement and will continue to strive to build on our success to date."
Ed Balls, the shadow Schools Secretary, said: "It is astonishing that the Prime Minister of our country should suggest that of the hundreds of brilliant state schools in London, none of them are good enough for him."