Local authorities in England say some parents are being “coerced” by schools into home educating their children, often before GCSE exams, and that there has been a sharp increase in the number of pupils being removed, according to the government’s admissions watchdog.

The annual report of the Office of the Schools Adjudicator (OSA) says more than 52,000 children were registered as being home schooled in 2017-18, using figures supplied by the 152 local education authorities in England. But it notes that, because there is no requirement on parents to register, the figure is an underestimate of the real total.

The figure represents a steep increase from a similar survey in 2015-16 that estimated about 37,000 school-aged children were registered as home educated.

Shan Scott, the chief schools adjudicator, said some local authorities had reported substantial increases “of between 40% to 70% in recent years in the numbers of children electively home educated”.

One local authority told the OSA it had received more than 1,000 new registrations in the course of the 2017-18 academic year, and said “many of these are instantly identifiable as inappropriate”.

Councils reported that parents had a variety of reasons for home education, including the failure to secure a place at a preferred school. One local authority said that alone accounted for 9% of all home schooling decisions.

But “off-rolling” – the practice of a school shifting pupils off its rolls without using formal exclusion processes – was also said to be widespread.

“In a story echoed by other local authorities, one said ‘it is reported by parents that they have been coerced to become electively home educated’ with some reported instances of schools preparing a standard letter for parents to sign advising of their intention to electively home educate,” the OSA report says.

Scott added: “I was told that that there tended to be an increase in moves towards elective home education during the key stage 4 years.” Key stage 4 – years 10 and 11 – are when pupils study for and sit GCSE exams.

The OSA report is the latest evidence of increasing concerns over off-rolling, whether for behavioural or academic reasons. Earlier this week Ofsted announced it would use data to spotlight schools that appeared to be off-rolling pupils, with schools doing so at risk of being downgraded by inspectors.

An investigation by the Guardian found that a high-flying grammar school in Bromley, St Olave’s, had been acting unlawfully by pushing out pupils in its sixth form whom it feared might not get top A-level grades and so damage its league table ranking.

The OSA also said parents opted for home education because of their child’s anxiety or unhappiness at school, especially as a result of bullying, or concerns about the standard of education. Others said they did so because their child’s special education needs were not being met.

One local authority told the OSA: “It is felt to be too easy for parents to elect for home education. This is often done by parents who have no idea of what home education involves, often done in haste after a minor falling-out with the school.”

The Department for Education last year called for evidence on home schooling practices, and is soon to publish guidance for parents and local authorities that may include compulsory registration.

“It was clear to me that many local authorities believe that a requirement for home educating parents to register with the local authority would do much to safeguard children,” Scott said.

The report also suggested grammar schools were still not doing enough to recruit pupils from disadvantaged backgrounds, despite 118 selective schools now giving priority to pupils on free school meals in their admissions process.

“In some – but not all – cases, there is concern that the proportion of children eligible for the pupil premium securing places at the schools has not increased in the ways hoped for,” Scott said.