Research into “off-rolling” from schools in England has found the scale of the problem may be worse than previously thought, with one in 10 secondary pupils removed from the rolls without explanation.

Researchers from the Education Policy Institute (EPI) found that more than 61,000 pupils out of the national cohort who sat their GCSEs in 2017 experienced an “unexplained exit” at some point during their secondary school career. Of these, two out of five never returned to school again.

The overwhelming majority of those affected were from the most vulnerable groups, including pupils with special educational needs and disabilities (SEND), those receiving free school meals or those in the care of the local authority.

According to the EPI, while a proportion of those unexplained exits will be legitimate decisions made in the interests of the child, others are the result of schools – under pressure from government and amid increased scrutiny of league tables – deliberately gaming the system by offloading challenging students to boost GCSE results.

Mary Bousted, the joint general secretary of the National Education Union, said the EPI findings were shocking and called on the government to take action. “That pupils with complex needs are most likely to fall out of the school system shows that, as a country, we are failing our most vulnerable children.”

The education secretary, Gavin Williamson, said he had asked officials to look into the issue of off-rolling. “Obviously this is something that is always of concern; it’s something I have instructed the department to look into very closely,” he said.

Researchers found multi-academy trusts and local authority schools with higher than average unexplained exit rates. The report points out that all larger multi-academy trusts – with 10 schools or more – had above-average rates, while nearly all also had higher than average rates of permanent exclusion.

Pupils were at least twice as likely to experience an unexplained exit than the average in more than a dozen school groups. Rosedale Hewens academy trust in Hillingdon, west London, had the highest rates of unexplained exits by a significant margin, at six times the average.

The chair, Marie Ashley, denied that any pupils had been off-rolled, but explained that the trust offered a flexible approach to learning, which allowed some students longer to complete their GCSE courses, distorting figures but allowing an inclusive approach.

“This research shows that there are thousands of pupils in England routinely removed from schools with no apparent explanation,” the report’s author, Jo Hutchinson, said. “The overwhelming majority of exits from school rolls are experienced by more vulnerable pupils, such as those with special educational needs and disabilities.

“The government should reduce perverse incentives for schools and do more to promote inclusion – only then will it help to prevent those with more complex needs from being moved around the system.”

The study updates earlier EPI research, published in April and based on the same data, which found that 1 in 12 pupils (49,000 in total) from the 2017 cohort were removed from rolls at some point for unknown reasons. Researchers have since refined their methodology and say the new report presents a more accurate picture. The latest figures represent an increase of just over one percentage point from 2014.

Geoff Barton, the general secretary of the Association of School and College Leaders, said: “It is right to use this analysis to ask questions but we would urge commentators not to jump to conclusions about particular trusts or local authorities or to try to score political points.

“What is clear is that we need a system of measuring school performance which rewards the inclusion of vulnerable pupils rather than the current system which effectively penalises schools with inclusive intakes because these pupils tend to make less progress than their peers.”

A Department for Education spokesperson said it was against the law to remove pupils on the basis of academic results. “Any school that does this is simply breaking the law, but unexplained pupil exits is not the same as off-rolling … we will continue to work with Ofsted to tackle off-rolling in any setting.”