Another 131 free schools have been approved to open in England, creating about 69,000 places.
They will include a non-selective school in Dartford opened by an academy trust with runs grammar schools.
All new state schools are now opened under the free school scheme – which can be run by academy trusts, parents or community organisations.
The Education Secretary Justine Greening said they would help to “give parents more choices”.
But Labour said the free school project had been “expensive and inefficient”.
The biggest number of these new schools will be in the south east, with more than 15,000 places in 27 schools, followed by almost 10,000 extra places in London in 18 schools, and 9,000 places in 12 schools in the west Midlands.
The new schools include 20 schools for children with special educational needs, which are being opened by local authorities, but as part of the free schools programme.
A list of free schools open or in the “pre-opening” stage, up to April 2017, published by the Department for Education, now shows about 800 schools.
Hundreds of thousands of additional places are needed for a rising school-age population.
If the government achieves its separate aim of opening a new generation of grammar schools, then the next wave of free schools could include selective places.
In this latest announcement, the Endeavour Multi-Academy Trust, which runs two grammar schools, is to open a non-selective secondary free school in Dartford.
Kevin Courtney, leader of the National Union of Teachers, said: “At a time when the majority of schools are struggling to survive the decision to pour tens of millions of pounds of taxpayers’ money into free schools, for some to be sponsored by grammar schools is indefensible.”
Among the new schools will be Working Title, a sixth form in north London specialising in film.
There will also be St Bede’s Inter-Church School, a secondary school in Cambridgeshire, supported by both Anglican and Catholic dioceses.
Toby Young, director of the New Schools Network which promotes the setting up of free schools, said free schools would provide 400,000 places when full and had become “a permanent part of England’s educational landscape”.
But Labour’s shadow education secretary, Angela Rayner, warned: “The free schools programme has been proven to be an enormously expensive and inefficient way to create school places.
“The Tories need to look again at school place planning, and makes sure that taxpayers are getting value for money.”
A recent report from the National Audit Office questioned the cost of free schools and purchasing of land.
It reported that opening 833 free schools by 2021 would cost £9.7bn.
Education Secretary Justine Greening said the new schools would “give us the school places we need for the future, and they also give parents more choices to find a great school place in their area that’s right for their child”.