Ofsted has rated three-quarters of the first 24 free schools 'good' or 'outstanding'.
They include Canary Wharf College, London, which has a Christian ethos and was one of the four free schools rated 'outstanding'.
Schools with the top rating impressed Ofsted inspectors in the four categories of: achievement of pupils, quality of teaching, behaviour and safety of pupils, and leadership and management.
Among the 14 rated 'good' was St Luke's Church of England Primary, which was opened last September by the Bishop of London. St Luke's is the first Church of England free school and there are plans for six in total across the capital.
Five schools were rated as 'requires improvement'. The only new free school to be rated 'inadequate' was Discovery New School, West Sussex, a Montessori primary school with a Christian character "in the Anglican tradition".
The schools with the lower ratings will be expected to take steps to ensure a "swift turnaround", the Government said, with the possibility of the school being closed down or handed over to a high-performing sponsor or existing school.
The Government's new free schools are state-funded but independent of local authority control, being run by charities, parents and faith groups. They are free to decide their curriculum and can also choose how long their school day and terms are.
The free schools have been open less than two years and have faced strong opposition, with challenges raised over their accountability, location, and the groups running the schools.
However, the Government said the Ofsted reports were an "encouraging start" to the free schools programme.
Education Secretary Michael Gove said: "Too often the best schools are only available to the rich who can afford to go private or pay for an expensive house in the catchment area of a good school. Free schools are giving all parents – not just the rich – the choice of a high-quality school with great teaching and strong discipline."
There are 81 open free schools, with around a further 200 planning to open from September.