Despite concerns among local authorities that the ongoing squeeze on budgets is placing increasing pressure on frontline services, the DfE's position in recent years has been that there is no evidence that spending more money improves effectiveness.
It argues that the fact that some authorities with lower per-head spend on children's social care achieve better outcomes than those spending more money indicates that, rather than additional funding being required, further efficiencies can be found.
However, research commissioned by the LGA has found that the main drivers of the cost of children's services are largely beyond the control of councils.
The study, conducted by the consultancy firm Newton found that children's services spending by English councils in 2016/17 varied from £292 to £1,254 per child and young person.
Newton's analysis concluded that half of this variation was caused by five factors: levels of deprivation; crime rates; disposable household income; the level of unemployment; and size of the population under the age of 26.
Deprivation was the single biggest of these factors, accounting for 31 per cent of the variation in council spending. Together the five factors altered council spending by £334 to £883 per child.
"These factors are largely outside of the control of councils, and certainly sit outside the control of children's services," the report states.
"As a consequence, variation in what authorities spend on children's services (per head of child population) is inevitable. It is not logical to expect authorities to converge on a single ‘right' value of spend."
Richard Watts, chair of the LGA's children and young people board, said the study "comprehensively disproves the notion" that the variation "is simply a result of inefficiency or poor practice".
"We are regularly quoted statistics which show some children's services departments are spending considerably more than others, with the clear suggestion that higher spenders should be able to reduce their budgets to match those of lower spending areas elsewhere," he said.
"The research shows that such arguments are misguided and shortsighted, explaining for the first time why variation is an inevitable result of the specific circumstances facing individual councils."
In recent years the DfE has repeatedly argued that there is limited or no relationship between spending on children's services and good outcomes for children.
In March, children's minister Nadhim Zahawi said there is "very little correlation" between the two. In January 2016, the DfE told the education select committee that there is no link between the amount local authorities spend on children's social care and the effectiveness of services.
Stuart Gallimore, president of the Association of Directors of Children's Services, said the findings underline the need for the government to address the predicted £2bn shortfall in children's services budgets by 2020.
"There are two clear things I take away from the report: it demonstrates impact of levels of poverty and deprivation and that variation in spend is due to a variety of factors which are largely out of the control of individual local authorities, busting the myth that there is enough money in the system, there is not," he said.
"The government urgently needs to recognise the challenges we face and act before it is too late by plugging the £2bn funding gap in children services, committing to a preventative approach to improving children's outcomes and the development of a cross-departmental child poverty reduction strategy."
The research suggested that the national variation in spending per child could be reduced by 13 per cent if councils adopted the "right" steps to improving outcomes for children and young people but warned that the changes this would require could be expensive and difficult to implement.
These changes include reducing the number of children taken into care through earlier intervention, preventing drift in casework, better matching of looked-after children with placements, and putting children on the "best level of support or type of plan" after they are assessed by social workers.
However, Newton added that the data it analysed meant it could not determine whether there is a link between greater spending on early help services and lower spending on looked-after children and safeguarding.
The study also said that the different accounting methodologies used by councils explain little of the variation in spending.
The Department for Education has been contacted for comment.
The Local Government Association and Newton Europe will give a presentation on the research at CYP Now's Early Help conference, taking place on 19 September. See who's speaking, and book a place here.