The UK's schools watchdog, Ofsted, believe head teachers have come under growing pressure from parents or religious leaders to change uniform regulations.
They fear the move is divisive as it sexualises young girls because the hijab is traditionally not worn until puberty.
"While it is for schools to determine their uniform rules in accordance with the law, there is growing concern about the hijab appearing in a primary school uniform list. We are looking at whether there is evidence that schools are facing external pressure to adapt their policies," an Ofsted source told 'The Sunday Times', which carried out the survey.
Campaigners want the UK government to issue guidance making it clear the hijab has no place in primary schools and for inspectors to report on those that allow it.
More From This Section
"Schools are allowing it because they are afraid of being called Islamophobic and they have been told that this is a religious garment - but they need to support Muslim girls to have free choices, not to be set apart from other children," Gina Khan, a children's rights campaigner in Birmingham, said.
In Tower Hamlets, east London, 34 per cent of 68 primaries had an online headscarf policy and in Luton in the east of England the figure was 36 per cent.
But in some other areas with large Muslim communities the practice has not taken hold. Only 6 per cent of 77 primary schools surveyed in Leicester included the hijab in the online list of approved items, and in Manchester eight out of 133 schools did so (6 per cent).
"If a school decided to allow a pupil to wear a burqa, that would be up to the school," a spokesperson said.