Three-quarters of the first free schools to open have been rated as good or outstanding, according to official figures.
Six did not reach this standard, with one declared inadequate by inspectors.
All of the first 24 flagship free schools, which opened in 2011, have now been inspected by Ofsted, the Department for Education (DfE) said.
Of these, four were rated outstanding, 14 were found to be good, five were judged to require improvement, and one was inadequate.
The DfE said the results were an "encouraging start" to the Government's free schools programme, and insisted that those not judged as good or outstanding will be expected to take action to swiftly turn them around.
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."
The figures broadly reflect the ratings of state schools across England. Ofsted data show that as of March 31, 22% of all state primary and secondary schools in England were rated as outstanding, 57% were good, 19% were found to be satisfactory or require improvement and three per cent were inadequate.
"Requires improvement" replaced satisfactory as a judgment last September. In total, there are now 81 open free schools - semi-independent state schools set up by groups including teachers, parents, educational organisations and charities. Around 200 more are expected to open from this September.
All Saints Junior School, Reading - outstanding; ARK Atwood Primary Academy, central London - outstanding; ARK Conway Primary Academy, west London - outstanding; Canary Wharf College, east London - outstanding; Barnfield Moorlands Free School, Luton - good; Bristol Free School, Bristol - good; Eden Primary School, north east London - good; Etz Chaim Jewish Primary School, Barnet - good; Krishna-Avanti Primary School, Leicester - good; Langley Hall Primary Academy, Slough - good; Maharishi Free School, Lancashire - good; Rainbow Primary School, Bradford - good; St Luke's Church of England Primary, north London - good; Stour Valley Community School, Suffolk - good; The Aldborough E-ACT Free School, east London - good; The Free School Norwich, Norfolk - good; West London Free School, west London - good; Woodpecker Hall Primary Academy, north London - good; Batley Grammar School, West Yorkshire - requires improvement; Kings Science Academy, Bradford - requires improvement; Nishkam Free School, Birmingham - requires improvement; Priors Free School, Warwickshire - requires improvement; Sandbach School, Cheshire - requires improvement; Discovery New School, West Sussex - inadequate.