No one has the power to close illegal schools, the head of Ofsted has admitted, as it emerged that a headteacher who has been prosecuted vowed to continue operating.

Amanda Spielman, the chief inspector, said that inspectors, local authorities and the Department for Education are all unable to shut down unregistered schools even when they are breaking the law.

Her comments came after Nadia Ali, the headmistress of Ambassadors High in Streatham, south London, said the school will remain open.

Last month Ms Ali and her father were both convicted under section 96 of the Education and Skills Act after a court heard that they were running a full-time school “without the legal authority to do so”.

The south London school, which describes itself as having an Islamic ethos, says it charges £2,500 a year per pupil and had 45 children on the roll at the time of its last inspection.

But it has not yet met standards required to register. But Ms Ali said that her pupils were "happy learners" and denied she was breaking the law, as the school is now open 18 hours a week.

Ofsted inspectors found that the school had "wilfully neglected" safeguarding and that almost half of its teachers had not undergone criminal record checks.