The Education Secretary has dismissed claims that there would not be enough primary school places for pupils in two years time.
Michael Gove said there were no problems with primary school places this year and pledged that every child would have a good school place in years to come.
It comes as council leaders warned that a dramatic rise in demand could see some parts of England with more primary pupils than places in two years time.
Speaking as he officially opened Perry Beeches III free school in Birmingham along with Prime Minister David Cameron, Mr Gove said: "We haven't had what Labour predicted, which are problems with primary school places, even though they were the people who failed to invest in primary schools last time around, wasted money on vanity projects."
Mr Gove continued: "We've had to clear up that mess. That is why every parent is getting their child a good school place this year and that is why in the years to come investment that we've made will ensure that education continues to improve."
During the visit, Mr Cameron said some £5 billion was being spent on providing extra primary school places between now and 2015.
Mr Gove said: "Every child has a safe and secure place. Every child will be educated in a school I believe where ambition has never been higher and a determination to overcome the accidents of birth that have held children back in the past is shared by the professionals and by the Government."
It comes as the Local Government Association (LGA) claimed as many as two in three councils could see more children looking to start primary school in their area by September 2016 than there are currently places for.
The LGA warned that schools are already having to convert non-classroom space such as music rooms and libraries into classrooms and others have been forced to reduce playground sizes.
David Simmonds, chairman of the LGA's children and young people board, warned of a "desperate" shortage of school places.