The education secretary, Damian Hinds, has called on headteachers in England to expel fewer pupils, as an independent study revealed that almost eight out of 10 children who are permanently excluded come from vulnerable backgrounds.

The long-awaited review of exclusions in England, carried out by a former minister for children and families at the Department for Education, Edward Timpson, and published on Tuesday, found that 78% of expelled pupils either had special educational needs (SEN), were eligible for free school meals (FSM) or were “in need”.

It found that boys with social, emotional and mental health difficulties were 3.8 times more likely to be permanently excluded than a child without SEN, and children from the most disadvantaged families were 45% more likely to be excluded than other pupils.

Children from some ethnic backgrounds were also over-represented in exclusion figures. After accounting for other factors, pupils from a black Caribbean background were 1.7 times more likely to be permanently excluded than white British children, while children from Indian and Bangladeshi backgrounds were half as likely to be permanently excluded as their white peers.

The review was broadly welcomed across the sector, but school leaders said it failed to address the funding crisis in schools, which they say is contributing to increased exclusions. The Department for Education (DfE) is currently preparing its bid for more funding in the autumn spending review.

“The current level of funding is so desperately inadequate that many schools have had to cut back on support staff who provide early intervention to children with challenging behaviour,” said Geoff Barton, the general secretary of the Association of School and College Leaders.

“This makes it more difficult to prevent challenging behaviour escalating to the point of exclusion, and we believe this has fuelled the rise in the rate of exclusions in recent years.”

Hinds confirmed that the government would act on the review’s recommendation that schools should in future be made accountable for the pupils they permanently exclude. A consultation will be launched later this year to work out the most effective way ahead, possibly leading to reform of commissioning and funding arrangements for alternative provision after exclusion.

There will be a crackdown on “off-rolling”, whereby a school illegally removes a pupil from the register without formally excluding them. Hinds acknowledged it was happening but said it was “on a relatively small scale. Where it does exist, it’s a matter of concern.”

He said: “I would like to see the level of exclusions to come down. It’s lower than it was 10 years ago, but I would like to see the level of exclusions coming down further.” Following years of decline, rates of both fixed-term and permanent exclusion have risen since 2013-14, with 40 pupils expelled every schoolday, according to latest figures.

Hinds nevertheless made it clear that headteachers should retain the right to exclude pupils as a last resort, in order to protect the other children in the class as well as teachers. “It has to be there as an option,” he said. “But if a child is going to be excluded, it’s important they are not excluded from education as a whole. Leaving one school has got to be the start of something more positive.”

The children’s charity Coram, which contributed pupil and parent views of school exclusions to the review, identified “a worrying lack of support” for expelled children and their families.

More than 80% of parents of children who were permanently excluded said the support they received in finding an alternative school place for their child was poor or very poor. Some said their children had been affected by anxiety, depression, and loss of self-worth.

One parent said of their son: “The decline in his mental health is hugely apparent. He has become very reclusive and has only left the house four or five times in the past four weeks.” The stress of the exclusion also took its toll on parents. “My husband and I have lost significant work days and salary as a result,” said one. “As a family, we are at breaking point.”

Timpson’s landmark study, which makes 30 recommendations, found huge variation across the school system. Overall, 85% of all mainstream schools did not expel a single child in 2016-7, while 47 individual secondary schools (0.2% of all schools) expelled more than 10 pupils in the same year.

“We expect school leaders to make sure all children are getting a good education, but we must equip them with the skills and capacity to do so,” Timpson said. “We need to reward schools who are doing this well and hold to account those who are not. Most importantly, there must be safeguards in place for when things go wrong so that we can keep children on the path towards the successful future they all deserve.”

The DfE made clear there were no plans to limit the number of exclusions. Schools will, however, be supported to use them effectively and encouraged to intervene early to avoid exclusions later on. The government also plans to rewrite guidance on managing behaviour, including the use of isolation units in schools and support for those with SEN, and has promised to improve the quality of alternative provision.