In its new report, Free Schools: the Next 10 Years, The New Schools Network (NSN) says the controversial programme - introduced under the Conservative and Liberal Democrat coalition government - has lost momentum because criteria for the most recent waves of free school applications were too stringent.
It also calls for dozens of failing academies awaiting a new sponsor to be handed to community organisations to run.
However, teachers' unions have criticised the proposal.
NSN called on the government to recommit to opening 100 new free schools a year, with greater emphasis placed on creating capacity in areas where education standards are deemed to be poor - currently, free school applications prioritise areas with insufficient places.
"Building new schools shouldn't just be about meeting the basic need for new school places, but ensuring every child has a good school place," the report states.
"That is the only way we will tackle chronic underperformance and spread educational excellence.
"It is important that free schools are located in areas of need, but that must mean educational as well as demographic need. It is no good simply to say to parents ‘there are places available in an underperforming school'."
NSN also noted that in 2017, more than 10,000 new places were created in schools rated either "inadequate" or "requires improvement" by Ofsted.
It called this "not acceptable", and instead said a new free school would better serve the needs of the local area and create choice and competition.
NSN said the 93 "orphan" schools rated inadequate by Ofsted should be taken over by parent and community groups rather than wait any longer for a suitable academy sponsor.
However, Dr Mary Bousted, joint general secretary of the National Education Union, said it was "beyond parody" that the NSN should do this, given its dependence on DfE funding.
"The fact that so many schools are ‘awaiting' a sponsor and are effectively in limbo is a searing indictment of the dysfunctional academies and free schools policies which the NSN promotes," she said.
"The ridiculous dogma that academisation is the answer needs to be abandoned. There is no evidence that academy sponsorship improves pupil outcomes and forced academisation is both disruptive and anti-democratic.
"We need a supportive and co-operative framework for school improvement, involving the local authority and neighbouring schools in full consultation with parents and staff. Parachuting in NSN-approved groups to take over schools would be a recipe for disaster."