David Cameron has instructed the cabinet secretary, Sir Jeremy Heywood, to conduct an investigation into the roots of the row between Theresa May and Michael Gove over the government's strategy on tackling Islamist extremism.

In a sign of the prime minister's anger after the row overshadowed the Queen's speech on Wednesday, Heywood is to hold separate interviews with the two ministers, who are both on course to be rebuked by Cameron.

The disclosure of Heywood's involvement came as a Birmingham school at the centre of the alleged takeover plot by Islamists was branded inadequate by Ofsted inspectors for doing "too little to keep students safe from the risks associated with extremist views".

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