David Cameron has insisted that the Government's free schools programme is a "great success".
Many of the new schools are "massively oversubscribed" and are driving up standards elsewhere, the prime minister said. The government announced on Friday that it has approved applications for a further 102 free schools to open from September 2013 onwards.
Unveiling the list at Woodpecker Hall Primary Academy in north London - one of the first 24 free schools to open last autumn - Mr Cameron said: "I think it's been a great success.
"What we are seeing is real quality, real choice for parents and it's a great part of our school improvement programme.
"Many more children are getting the education they, and their parents, want and deserve."
Free schools are established by groups including parents, teachers, faith groups and charities and have powers to decide how they spend their budgets and set their own curriculum, teaching hours and term times.
But teaching unions have claimed that they adversely affect neighbouring schools when they open in areas with no shortage of spaces.
One free school, at Beccles in Suffolk, sparked controversy last month when it emerged it had received just 37 applications for 162 places when it opens this September.
Mr Cameron said: "Almost all free schools are over subscribed."
He added that they are "really delivering" in terms of quality and competition, driving up quality elsewhere.
"The problem in our education system has always been that while there are good schools, there aren't enough good school places."
Free schools are addressing that issue, Mr Cameron said.
Earlier, the Prime Minister met reception year children at Woodpecker school, where they asked him about the fun parts of his day.
Mr Cameron replied that living in Downing Street above his offices, means that he get to see his children, Nancy, Elwen and Florence, every day "no matter how hard I'm working".
He also told the youngsters that his favourite subject at school had been history.
Around 50 free schools are due to open this autumn.
The Department for Education said 88% of the primaries approved today for next year onwards are in areas with a shortfall of places and 63% in an area with a severe need for more places.
Some 67% of mainstream schools approved are in the 50% most deprived communities in the country. And there will be five special schools and 12 "alternative provision" schools to educate vulnerable children.
Shadow education secretary Stephen Twigg said: "We support new schools being established and wish these schools every success.
"However, the government must ensure these are in places where there is real demand from parents and a need for new places.
"The first duty of the education secretary is to ensure there are enough school places. So the free schools need to be in the right areas of the country, not just approved in a haphazard way."