The Local Government Association said a £600m reduction in the education services grant (ESG) from central government, which covers the cost of such work, will mean many councils will no longer have the money to fund them.
Meanwhile, a change to regulations will mean councils can only undertake the duties if the school agrees to cover the cost from its own budget.
The LGA said the changes could affect a range of support services for schools, including criminal record checks on staff, safeguarding and mental health support.
It is claiming this will place more than five million pupils at risk "as schools are forced to decide what services they are able to maintain".
Other services affected by the change to the ESG include student welfare, fire safety, air quality as well as building and playing field maintenance.
Richard Watts, chair of the LGA's children and young people board said: "Services that were previously provided to schools by councils will become an extra burden for schools, putting additional pressure on already overstretched budgets."
Despite responsibility for funding these services shifting from councils to schools, local authorities will still be legally obliged to provide them. This leaves councils at risk of failing to fulfill their statutory obligations, adds Watts.
"Councils have their hands tied. They are legally obliged to provide these services but will have no money to do so unless the school is prepared to pay for it from its own pocket.
"Councils are committed to ensuring all children get access to high-quality education and that they can do so in a safe and healthy environment. Changes to regulations and school funding mean that councils could fail to meet their legal duties, which protect children and teachers whilst at school," Watts added.
In December 2015 the government announced that the education services grant, which also provides school improvement services, would be cut by £600m over five years.
The LGA has also reiterated calls it made in November last year, for the cut to be reversed.