Downing Street has ordered a system of snap inspections in response to allegations that a cluster of schools in Birmingham are under the influence of Islamist extremists.

Arguing that the schools in question have been able to "cover up" because they had notice of previous inspections, David Cameron announced proposals to send Ofsted to any school without warning.

The prime minister's intervention comes as Ofsted publishes a string of reports triggered by the so-called "Trojan horse" letter alleging that there had been an Islamist takeover plot to take control of community schools in Birmingham. Five Birmingham schools out of 21 inspected will be downgraded to inadequate – Ofsted's lowest rating – and placed in special measures on Monday, after what inspectors claimed was poor management and lack of attention to protecting pupils from what Ofsted will call "an awareness of the risks arising from extremism".

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