Services are threatened unless town halls receive billions in extra funding, the umbrella group has warned.
The LGA outlined its position in its submission for the Autumn Budget, which was published on Friday last week.
It stated: “It is vital that the budget recognises that councils cannot continue without sufficient and sustainable resources.
“Services such as children’s services, adult social care and homelessness are at a tipping point.”
The document said councils will have lost £16bn in core government funding between 2010 and 2020, while local authorities drew on more than £600m from their reserves in 2016/17.
It also noted that the biggest area of financial challenge for councils was children’s social care services.
Analysis by the association showed that 75% of councils were forced to overspend at least £500,000 on their children’s services budgets in order to protect vulnerable youngsters in 2015/16.
The overall children’s services budget was overshot by £605m in that year as demand for services surged.
The LGA added: “Councils are also facing additional costs, such as the pay pressures related to the introduction of the National Living Wage, paying for sleep-in carers and the unexpected, but essential, costs for replacing cladding systems following the Grenfell Tower tragedy.”
Following official combustibility tests the LGA stated cladding on 45 tower blocks owned by 15 councils will need to be removed and replaced – which is likely to cost millions.
The body, which represents 415 authorities, also said pay pressures from the National Living Wage, changes to public sector pay policy and fire-safety renovations in the wake of Grenfell should be met by the government in full.
It also suggested the government needed to bring forward devolution of business rates, remove significant central controls on council tax and match fund £8.4bn of EU funding.
