The whole school needs to be involved, inspectors say
Schools which most successfully revive after being labelled failures have strong leadership, self-knowledge and sense of identity, Ofsted says.
The English education inspectorate said the foundation for improvement was honest and accurate self-assessment, a theme now common around the UK.
Involving pupils as "stakeholders", through a school council, house system or open forum, was crucial, it said.
Continuous review was common in "the relentless pursuit of excellence".
Ofsted has been promoting the importance of self-evaluation for a decade but the latest inspection regime makes it central - with visits by external inspectors being a check on the quality of what managers have done internally.
All schools now have to maintain a self-evaluation form - known as the "Sef" - which is the basis for the inspection visit.
"There is no perfect Sef and inspectors know this," Ofsted says. It should:
convey a clear picture of how well the school is doing
provide proof of how you know what you know
show what you are doing to build on successes and remedy weaknesses"
Ofsted's report is based on 14 schools in England previously deemed to require "special measures" - in other words they were failing to provide an acceptable standard of education.
When re-inspected they were showing continuous improvement.
"The schools became successful in unlocking the potential of all groups of pupils and students," Ofsted said.
"All the actions contributed to the development of a whole-school identity and sense of belonging. There was evident pride in recognising collective achievement."
The report adds: "The associated improvements in personal development, especially behaviour, were dramatic."
"The message from pupils and students who took part in the journey from special measures is powerful and unequivocal.
"They were in no doubt that the enjoyment of learning, achievement and well-being of every one of them mattered above all else in their schools."
Reinforcing the message about self-improvement, the report says outside help can actually make things worse.
"Unless external support for improvement was carefully matched to a school's particular circumstances and rigorously evaluated, it had the potential to create more problems and, at worst, to slow the pace of improvement."
Chief inspector Christine Gilbert said: "The report shows that if schools placed in special measures are willing to face up to the need for change and take appropriate action, they can improve very quickly and become outstanding schools."
The themes are becoming common in the UK's four education systems and indeed elsewhere in Europe.
In Scotland, HM Inspectorate of Education's self-evaluation toolkit for schools has a formal six-point scale and stresses what one education adviser calls the "so what" question: what difference did anything make to the quality of children's education?
Senior chief inspector Graham Donaldson talks of "the great strides taken by educational establishments in becoming aware of their own strengths and weaknesses, placing Scotland at the forefront of quality improvement internationally".
Northern Ireland's Education and Training Inspectorate has also found clear links between self-evaluation and improvement, so it forms the core of the education minister's proposed new school improvement policy.
In Wales, Estyn also stresses the need for good self-evaluation.
In a report earlier this year commissioned by the assembly government, it said schools should ensure pupils could be involved more in the self-evaluation, school improvement plans and decisions that affected their teaching and learning.