Private companies need incentives to dramatically increase the number of school places and make parental choice a reality, the Social Market Foundation said.
The think tank's proposals were presented to a seminar on Wednesday attended by senior government advisers, and have revived a political storm over the commercialisation of education.
Ministers were forced to deny last year that they would allow companies to profit from running academies after a leaked memo appeared to suggest that the idea had been considered.
The report from the free-market think tank, entitled "Supply side capacity in secondary education", said that student places need to be increased faster than the public sector can manage.
Private companies would pay half the capital costs of new, non-fee-paying schools, which would be funded on a per-pupil basis, making profits by running more efficiently.
Such a system has already worked in the US and Sweden, the report said.
Claudia Wood, researcher for the foundation, said: "We would, of course, have to ensure that schools created the profit via genuine efficiency gains rather than by simply cutting corners."
In Milwaukee, the report admits, the state government paid private schools $28 million (pound;14.5m) more than the cost of tuition in just two years.
Ms Wood also said that school organisation committees should be scrapped to allow popular schools to expand, and that the Government's present fast-track approach did not go far enough.
The report accepted that creating spare capacity above the 7 per cent that already exists might be seen as wasteful.
But it suggested that schools could be given flexibility to expand and contract each year according to demand. They might also share spare rooms or teaching staff to allow resources in short supply to go where they are needed.
The Conservatives outlined their own Right to Supply proposals to increase choice on Tuesday.
Faith groups, charities, profit-making companies and private schools would be eligible for public funding to expand or build new schools.
Tim Collins, shadow education secretary, said: "We do not take a view on the relative merits of charitable and commercial operators. We simply want to see more good school places."