Education Secretary Michael Gove blocked the introduction of "no-notice" inspections of schools two years ago, the head of Ofsted has claimed.
The chief inspector, Sir Michael Wilshaw, said he called for unannounced inspections when he first took up the post but that Gove rejected the idea because of concerns among headteachers.
Nick Clegg has also suggested that the government might have to look more widely at what is taught in schools such as academies, which currently have a high degree of autonomy.
In the Commons yesterday, the education secretary warned that all schools could now face no-notice inspections after an investigation into the alleged "Trojan Horse" plot by hardline Muslims to take over schools in Birmingham uncovered a "culture of fear and intimidation".
Sir Michael welcomed the announcement which he said represented a change of heart by Gove. "It is something that I called for two years ago when I first joined. That is something I discussed with the Secretary of State," he told BBC2's Newsnight.
"He said that we need to look at this and we need to listen to what headteachers are saying about needing to be in the school prior to the inspection so they can have a preliminary dialogue with the inspectors about how the inspection should be conducted. So we pulled back on that so they now have just a few hours.
"We had a robust discussion about it and I am really pleased that minds have been changed."
However the BBC quoted a senior Department for Education source as saying that Sir Michael was "wrong" to suggest that Gove had blocked no-notice inspections, adding: "We will say more on this soon."
Gove has already been involved in one bruising controversy over the issue of extremism in schools after a bitter row erupted last week - on the eve of the Queen's Speech - with Home Secretary Theresa May.
Following the intervention of a furious David Cameron, Gove was forced to issue a humiliating apology, while May lost her special adviser, Fiona Cunningham, who was forced to resign.
Gove said that all schools would in future be required actively to promote "British values" in the wake of the Ofsted investigation in Birmingham, which saw five schools placed in special measures.
Clegg told BBC Radio 4's Today programme this morning: "School autonomy is all very well until it is abused and that has clearly been the case here. That's why I think we need to get the balance right."
"I think many people will be surprised to know that some of these schools, while they are under a duty to deliver a balanced curriculum, they are not under any obligation to actually teach anything from the national curriculum whatsoever.
"Maybe one of the things that we need to think about is how do we make sure that ... a core curriculum, not a great sprawling one, is taught in all schools in our country regardless of the nameplate at the school gate.
"I think all parents would, broadly speaking, expect that their children are taught a core body of knowledge regardless of which school they are in. I think that might be one of the things we need to do in the future."
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