Speaking as he announced a range of new measures aimed at promoting integration and tackling radicalisation, Cameron said he would back “proper and sensible rules” made by institutions which could require women wearing a veil to show their face.
But he added he would not support a French-style ban on the burqa.
Cameron told the BBC on Monday: “I think in our country people should be free to wear what they like and, within limits, live how they like.
“What does matter, if for instance a school has a particular uniform policy, sensitively put in place and all the rest of it, and people want to flout that uniform policy, often for reasons that aren’t really connected with religion, I think you should always come down on the side of the school.”
He said that he would support the rights of any authorities to demand that a veil be removed.
“When coming into contact with an institution or you’re in court, or if you need to be able to see someone’s face at the border, then I will always back the authority and institution that have put in place proper and sensible rules.
“Going for the French approach of banning an item of clothing, I do not think that’s the way we do things in this country and I do not think that would help.”
Education Secretary Nicky Morgan also showed her support for banning the veil in all schools, further suggesting that teachers should be banned from wearing it. She told the BBC she agreed with the PM and said that uniform policy is “very much up to schools” to implement.
The prime minister was criticised by opponents, who suggested that he would “stigmatise” women.
Baroness Warsi, who served as the first female Muslim cabinet member, told the BBC on Monday that a veil ban was “lazy and sloppy,” and would mean implementing policies based on stereotypes which “badly stigmatise communities.”
Shadow Home Secretary Andy Burnham called the policy “clumsy.”
“[David Cameron’s] clumsy and simplistic approach to challenging extremism is unfairly stigmatising a whole community. There is a real danger that it could end up driving further radicalisation, rather than tackling it.”
Cameron’s remarks come as Morgan also unveiled a website which can be accessed by students and parents to learn about radicalisation and how to protect children from extremism.
The new Educate Against Hate site will offer advice based on resources and guidance drawn up by the government and charities including the NSPCC and Childnet, and will be officially launched at the Bethnal Green Academy in east London.