A report by Labour labels the situation across children's services as "unsustainable", pointing to the fact that last year saw the biggest rise in the number of children in care for seven years, with councils facing an estimated £2bn funding gap by 2020.
Labour has called on government to use next week's Spring Statement to provide the necessary funding to place children's services on a sustainable footing by "reversing tax giveaways to large banks".
"The situation across children's services is unsustainable, with a combination of reduced budgets and increasing demand," the report states.
"Government cuts to London boroughs and metropolitan councils means the rise in demand is pushing them towards the financial brink.
"The government must also commit to sustainable investment in preventative services as a matter of urgency."
Labour's warning coincides with a separate report by the National Audit Office, Financial Sustainability of Local Authorities 2018, which found that local authorities are struggling to juggle higher demands and cost pressures against significant central government funding cuts of nearly 50 per cent since 2010/11
"Many local authorities are relying on using their savings to fund local services and are overspending on services, which is not financially sustainable," the NAO said.
The report added that the Association of Directors of Children's Services and some authorities the NAO talked to have raised concerns about the long-term implications of reductions in spending on early years provision, such as Sure Start children's centres and services for young people, questioning whether there is a risk that this may be linked to increases in demand for children's social care services.
Ruth Allen, chief executive of the British Association of Social Workers, said: "The Labour Party's report on the funding crisis facing children's services in England makes for very difficult reading, unfortunately none of it surprising."
"Cuts to benefits, delays to Universal Credit and pressures on schools and the NHS are all pushing up demand on social workers who are overworked, overstretched and unsupported. This situation is untenable."