The Local Government Association (LGA) said councils are providing temporary housing for around 120,540 children with their families — a net increase of 32,650 or 37 percent since the second quarter of 2014.
It said the increase equates to an average of 906 extra children every month.
The LGA said placements in temporary accommodation can present serious challenges for families, from parents' employment and health to children's ability to focus on school studies and form friendships.
The LGA, which represents 350 councils across England, said the extra demand is increasing the pressure on local government.
It said councils need to be able to build more ‘genuinely affordable’ homes and provide the support that reduces the risk of homelessness.
This means councils being able to borrow to build and to keep 100 percent of the receipts of any home they sell to reinvest in new and existing housing, the LGA said.
Council leaders are also calling for access to funding to provide settled accommodation for families that become homeless.
Martin Tett, the LGA's housing spokesman, said: "When councils are having to house the equivalent of an extra secondary school's worth of pupils every month, and the net cost for councils of funding for temporary accommodation has tripled in the last three years, it's clear the current situation is unsustainable for councils, and disruptive for families.
"Councils are working hard to tackle homelessness, with some truly innovative work around the country — and we now need the government to support this local effort by allowing councils to invest in building genuinely affordable homes, and taking steps to adapt welfare reforms to ensure housing remains affordable for low-income families."
The LGA analyzed figures from the Department for Communities and Local Government (DCLG) for its findings.
A DCLG spokesman said the government is investing £550 million to help tackle the issue, adding: "The number of children living in temporary accommodation is down from its peak in 2006, but any increase in the number of homeless families is always a concern.
"We're clear that whilst temporary accommodation is vital in making sure that no family is without a roof over their head, councils have a responsibility to find secure, good quality accommodation as quickly as possible.
"The new Homelessness Reduction Act will also help individuals and families get the help they need earlier, stopping them becoming homeless in the first place."