Schools serving "insular" communities which also fail to promote "British values" are a cause for concern, Ofsted's national education director Sean Harford told a Lords committee today.
"The vast majority of schools are doing well in this area," Harford told the Lords committee on citizenship and civic engagement.
"We do have concerns over a very small minority of schools that are mainly in the independent sector."
He added that around 40 to 45 schools had been identified as inadequate in promoting British values, and had failed the Independent School Standards in this area.
"They are predominantly faith schools," said Mr Harford. "They tend to be serving communities that are quite insular anyway so need more promotion of fundamental British values than other communities where there are connections with the wider community."
He concluded that the teaching of British Values was: "mostly very good, but there is concern and acute concern in a small number of schools."
Ofsted does not inspect all independent schools.
Government guidance for maintained schools says they should promote the fundamental British values of democracy, the rule of law, individual liberty, and mutual respect and tolerance of those with different faiths and beliefs.
And the Independent School Standards also require independent schools to promote these values in order to meet the requirement to ensure the spiritual, moral, social and cultural development of pupils.