Cash-strapped councils could see their funding halved over the next two years, "threatening the existence" of vital services, the Local Government Association has warned.
Councils are facing a 54% reduction of £2.7 billion to their central government funding between 2018/19 and 2019/20.
Rubbish collections, road repairs, child services and care for elderly and disabled people would all be at risk if the cuts go ahead, according to the LGA.
Local authorities are already at "breaking point" and lack of funds could "threaten the existence" of some local services by 2020, a spokesman said.
Senior vice chairman Councillor Nick Forbes (pictured) said: "Rising demand and years of growing funding pressures have stretched councils to the limit.
"Councils knew they would struggle to cope with the pace of government funding cuts over the next few years.
"It was hoped that local government as a whole keeping all of its business rates income by 2020 would ease that pressure.
"With those plans now in doubt, councils are faced with the double jeopardy not only the money they have to pay for local services running out fast but also huge uncertainty about future funding after 2020."
The LGA is calling for the upcoming Local Government Finance Settlement to reduce the rate of cuts to core grant funding for councils in 2018/19 and 2019/20.
Around half of councils would no longer receive any this funding by 2019/20 and would also have to pay some extra business rates income back to the Government.
Mr Forbes said: "Councils face an overall £5.8 billion funding gap in just two years yet the budget disappointingly offered nothing to ease the financial pressure on local services.
"Our communities and the local services they rely on cannot take another two years of funding cuts with no solution in sight.
"The Local Government Finance Settlement must put this right."
The pace of these funding cuts was intended to coincide with local government as a whole keeping 100% of its business rates income by 2019/20.
These plans will no longer be in place by the end of the decade and remain in doubt after the Local Government Finance Bill, which was passing through parliament before the general election, was not reintroduced in the Queen's Speech.
Delays to the reforms mean councils are now heading towards a funding "cliff-edge" in two years which some councils and local services could be pushed over without urgent funding, the LGA said.
A Department for Communities and Local Government spokesman said: "With additional funding for adult social care announced at the Budget 2017, core spending power for councils has increased over the spending review period, giving them more than £200 billion and the certainty to plan ahead through our four-year funding settlement.
"Details of council funding for 2018/19 will be confirmed as part of the Local Government Finance Settlement."
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