Ofsted inspectors can downgrade schools for allowing staff and pupils to wear a face veil if it is a "barrier from learning", its chief inspector has announced.

Sir Michael Wilshaw has written to all inspectors instructing them to mark down institutions "if they judge the wearing of the veil is acting as a barrier to learning and to positive social interaction".

Under the new policy, schools will be judged "inadequate" if wearing a face veil on the part of pupils or staff is seen to be "hindering communication and effective teaching".

The Ofsted chief said he was concerned some heads were "coming under pressure" to relax a ban on veils. He said he wanted to reassure schools which ban or restrict veils they "can rely on my full backing for the stance they are taking".

"I am determined to ensure that discrimination, including on the grounds of gender, has no place in our classrooms," Wilshaw said in a statement.

"We want our schools, whether faith schools or non-faith schools, to prepare their pupils equally for life in 21st century Britain. We need to be confident our children's education and future prospects are not being harmed in any way."

The announcement came after the education secretary Nicky Morgan said it was up to schools to decide on uniform policies. However Ofsted's policy, which seemed to go further than Morgan's comments last week, received "full support" from the department for education.

A spokesperson for the Muslim Council of Britain said "accommodation" was needed over wearing the veil.

"It is a shame that the niqab - the full face veil that a minority of Muslim women wear - has become a polarising issue when it need not be."

Dr Sheik Howjat Ramzy, director of Iqra Institute in Oxford and former head of an Islamic school, went further and said the move was "unjust" and "picking on Muslims in particular".

"I believe he's totally wrong and this is totally unjust. Ofsted is picking on faith schools, specially Muslim schools. There is nothing wrong with wearing the head veil," he told the Daily Telegraph.

"Not many pupils wear the veil. The veil doesn't make pupils intelligent or not. It gives them their identity and some security. Pupils have the right to wear the veil if they go to Islamic schools. That is no problem."

Ofsted's latest controversial announcement comes amid an ongoing debate over whether it should be allowed to inspect out-of-school educational settings. A new policy from the education department would allow inspectors into any institution educating children for more than 6-8 hours a week.

However many MPs and church leaders have expressed concern this would mean churches and youth groups could face Ofsted inspections.