The Local Government Association has said that current levels of government funding are not enough to cover the extra costs involved in supporting the growing number of SEND pupils.
In addition to calling for extra funding, the organisation, which represents 370 councils, is calling on the government to rethink plans to prevent councils contributing money to ensure pupils with SEND receive effective support in schools.
The government has made proposals in its consultation on the high needs national funding formulae, that councils should not be allowed to "top up" funding shortfalls, but the LGA insists the practice has been an important tool for councils to help SEND pupils.
"Councils have had to meet the difference by topping-up high needs funding from other budgets where necessary, however the consultation suggests that this flexibility will no longer be available to local authorities, making it even more difficult to provide children with the support they need," a statement issued by the LGA said.
This will leave cash-strapped schools struggling to pick up the extra costs involved, the LGA has warned.
"If councils do not receive sufficient funding to cover high-cost SEND, they will not have the resources to allocate extra funds to highly inclusive schools that take higher than average numbers of pupils with additional needs," the LGA statement adds.
"Equally, mainstream schools may find it difficult to accept or keep pupils with SEND because they cannot afford to subsidise the provision from their own budgets, as they are already under significant pressure," the LGA statement adds.
The LGA acknowledges the government has provided some extra SEND funding over the last year, but is concerned this may not go to the areas most in need as it is allocated on the total number of children in an area rather than on the number of those with complex needs.
Richard Watts, chair of the LGA's children and young people board, said: "Whilst the additional funding announced earlier in the year was a step in the right direction, it was never enough to meet the needs of the increasing number of SEND pupils.
"Councils are doing all that they can to make sure children with SEND get the support and opportunities they need to flourish, but are experiencing increasing demand for all services. Proposed changes to schools and high needs funding could also make this problem even worse, taking away the freedom for councils to top-up high needs funding from other budgets if necessary.
"The reset of the high needs funding formula is the perfect opportunity for the government to ensure SEND pupils get the support they need to succeed at school."
Earlier this month the Department for Education announced that councils would share £215m in funding to create more school places and improve facilities for children with SEND.
This followed an announcement in January by children's minister Edward Timpson that £40m would be released for local authorities to help them transfer to a new assessment system, whereby all children with existing SEN statements must be evaluated through the new system of integrated education, health and care plans.