The inspectorate said tonight that routine inspections of schools early years, further education providers and social care settings would stop.
However any inspections triggered by safeguarding concerns will still take place, Ofsted told Tes.
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The watchdog revealed last week that schools could ask to defer inspections because of the impact of the coronavirus and that it would look favourably on all such requests.
And the Association of School and College Leaders and the NAHT's school leaders union also made the case for inspections to be halted when their leaders met with education secretary Gavin Williamson today.
An Ofsted spokesperson said: "Following the prime minister’s announcement this afternoon, we are putting a hold on all this week’s routine inspections of schools, social care, early years and further education providers. We are in discussions with the DfE about the longer-term picture.
Education secretary Gavin Williamson has said that he instructed chief inspector Amanda Spielman to suspend routine Ofsted inspections.
Ms Spielman said: "I’m grateful for the Secretary of State’s permission to suspend routine inspections. It’s clearly the right thing to do when teachers and social workers are under pressure as a result of the coronavirus outbreak. We all need to support them in their work.
“We will monitor what’s happening across education and social care and we will reserve the right to inspect where we believe the safety of children could be at risk, or we have other serious concerns. We will also continue to register and regulate social care providers, childminders and nurseries, so that these vital services can continue to support children and their families.”