David Cameron, the UK prime minister, has promised a "robust response" to allegations of "Islamic extremism" in schools.

Downing Street announced new steps on Monday to tackle the so-called Trojan Horse plot - reports of religious conservatives attempting to infiltrate schools in the city of Birmingham to make them adhere to a strict interpretation of Islam.

In a statement Cameron said: "Protecting our children is one of the first duties of government and that is why the issue of alleged Islamist extremism in Birmingham schools demands a robust response."

One of the measures is snap school inspections, the statement said, to counter findings that "notice periods were used to put on hastily arranged shows of cultural inclusivity".

Oldknow School, according to the Education Funding Agency, increased its teaching and discussion of Christianity for the benefit of inspectors.

Downing Street has said there will also be a special meeting of the government's Extremism Task Force to discuss investigations by the English education watchdog, Ofsted. The meeting on Monday will be attended by senior cabinet members.

Cameron's response precedes the publication of 21 separate inspection reports on Birmingham schools by Ofsted, which is also publishing an advice note to Michael Gove, UK education secretary.

He is expected to present his own report on Monday and has been criticised by Theresa May, the home secretary, for his response to Trojan Horse allegations.

Some of the schools said to be involved in the plot have rejected Ofsted's findings.

Park View Educational Trust hit back at the watchdog last Thursday.

It said inspections of Golden Hillock school were conducted in a climate created by the Trojan Horse letter and "unproven" allegations in media reports.