It’s a sunny, blustery day and four-year-old Thomas Tovell is well zipped into his anorak and wearing an expression of intense concentration as he helps a little gaggle of boys build a foam brick wall in his school’s outdoor learning area.

Thomas’s teaching assistant at Hilton primary school in Derbyshire, Rebecca Kerry, looks on and makes encouraging noises: Thomas has Down’s syndrome and Kerry is one of two who support him all day at school – one in the morning, one in the afternoon.

“He’s a lovely little boy,” she says. “He has a go at everything all the other children take part in. We do have to help him – he needs support with toileting and some observation over dinner. It’s really important that he has the support to make sure he can access everything another child would.”

But the brutal truth is that in a few months both he and his helper may no longer be here. All the school’s 50 teaching assistants – the equivalent of 12 full-timers – have received redundancy notices and a third of them will lose their jobs as the 850-pupil school struggles to plug a £120,000 hole in its budget. Thomas is one of four pupils the school would be unlikely to be able to support after such a large reduction in staff.

According to the Local Government Association (LGA), the body that represents local education authorities, this scenario is all too common. Pupils with special needs are at risk of being turned away from mainstream schools across the country. The irony of the situation, caused by real-terms cuts in school budgets combined with a rise in costs such as national insurance and pension contributions, is that educating pupils in special schools is generally more expensive. Costs vary across the country, but in Derbyshire the average cost of a primary place is £3,888 compared with about £10,000 for a special school place.

Kevan Lomas, headteacher at Hilton primary school: ‘We can’t just carry on doing what we have been doing on the basis of goodwill.’ Photograph: David Sillitoe/The Guardian

Hilton primary receives £8,000 for one-to-one support for Thomas’s education on top of the £3,900 it receives for each pupil. But the total cost of educating him is £24,245 – meaning the school must make up the shortfall of £12,345 a year.

The shortfall occurs in part because Derbyshire county council funds Thomas’s teaching assistant support for only 22 hours a week and the school has to find extra cash to top that up to the full 32.5 hours. It does this for many of the 82 pupils who receive special needs support. One boy whose parents would like him to go into reception class in September is likely to be funded for just 14 hours’ help even though he requires help with eating and toileting, cannot speak and has to be changed regularly because he tends to dribble.

Hilton’s headteacher, Kevan Lomas, says this bustling, happy school has been hit hard by the crisis.

“As a school we have a moral obligation to meet the needs of all children in our community. But we can’t just carry on doing what we have been doing on the basis of goodwill – our teaching assistants work well beyond the hours we pay them for,” he says.

As well as cuts and budget freezes, mainstream schools also have rising numbers of special needs pupils to contend with. The LGA points to official statistics that show a growing proportion of pupils with special needs are being educated in special schools – 8.5% in 2016, compared with 5.6% in 2012. Meanwhile there has also been a rise in the proportion educated in independent schools, from 4.5% to 6.3%.

Councillor Richard Watts, chair of the LGA’s children and young people board points to another problem. The government has proposed a new national funding formula for pupils with special needs, and this will leave local authorities with less flexibility. Traditionally, says Watts, local authorities have used money from their central budgets to subsidise special needs support. But in future schools will have the right to object to this, and to insist the money is used for other things.

All this adds up to an greater risk that mainstream schools will be reluctant to educate those pupils who need the most support, he says.

The Department for Education does not accept this argument. It has provided an extra £220m to support councils’ special needs provision this year and next, it says, plus a further £215m to help build classrooms and improve facilities.

“This government is determined to build a country where everyone can fulfil their potential. Schools are already funded to support pupils with special education needs and disability, and local authorities should provide additional funding when the cost of doing so is high. Under our proposals, no local authority will lose high needs funding and they will continue to have some flexibility to transfer funding from their schools to their high needs budgets,” a spokesman said.

Back in Derbyshire, where council officers have had many discussions with Hilton primary about its budget problems – and have given it £100,000 from contingency funds this year – the local authority says the answer is fairer central government funding for schools.

The council believes it might be able to find places in alternative mainstream schools for pupils who could no longer be supported at Hilton primary.

“We would ensure that the needs and wishes of families were fully considered in this process,” a spokesman said. “The council recognises the invaluable support that teaching assistants provide and also the difficult decisions that Hilton primary school are currently having to consider, although there are a number of other schools in a similar position. We will continue to work closely with Hilton primary to ensure we can find the best means of resolving its funding issues within the budgets available to us and to all schools in Derbyshire.”

Becky and Josie Smeathers. Photograph: David Sillitoe/The Guardian

At Hilton, parents are collecting their children at the end of the day. Year 6 has just arrived back from a residential trip, and those who accompanied them are looking forward to a few hours off. Among them is Becky Smeathers: she went with her daughter Josie, who has cerebral palsy.

Smeathers feels Josie has been lucky – she’s been given support to help her attend her local school throughout her primary years, helped by a significant top-up from the school’s central budget on top of what the local authority pays: the school provides support for 32.5 hours a week for Josie even though she’s funded for only 22. But others coming later may not be so fortunate.

“Josie has selective mutism and doesn’t communicate with any of the classroom teachers. She can’t go to the toilet by herself and she can’t put her hand up to ask to go. If her pencil falls on the floor she can’t get it. She has good friends but it isn’t their role to do that.

“If she didn’t have the extra hours’ support I would have to move her to a special school. She wouldn’t cope in a class of 30-plus children.”

Josie has benefited enormously from being here, her mother says: “She has been able to integrate and to communicate with the other children. She has a real laugh; she has a great sense of humour. Without that extra support, she would be excluded from those sorts of opportunities.”