Local authorities are facing a £5.8 billion black hole in their budgets that not even closing every children's centre, library, leisure centre and turning off every street light could fill, council leaders have warned.
Unless they are given access to more money, English councils will have lost 75p out of every £1 they received in core central government funding by 2020, the Local Government Association said.
The LGA is now pressing the Government to lift the cap on council tax which means authorities must seek approval through a local referendum if they want to raise it by 2% or more.
It also wants councils to keep all of the £26 billion they collect each year in business rates as would have happened under the Local Government Finance Bill which was introduced in the last parliament.
However, the bill failed to complete its passage before Theresa May called her snap General Election.
And it was not re-introduced in last week's Queen's Speech, raising doubts as to whether 100% business rate retention will now go ahead.
In a speech at the LGA's annual conference in Birmingham, Chairman Lord Porter of Spalding will say: "Councils can no longer be expected to run our vital local services on a shoestring.
"We must shout from the roof tops for local government to be put back on a sustainable financial footing.
"Councils are the ones who can be trusted to make a difference to people's lives.
"If austerity is coming to an end, then we need to make sure councils are at the front of the queue for more money.
"Only with adequate funding and the right powers can councils help the Government tackle the challenges facing our nation now and in the future."
A Government spokesman said councils had been given the "vital certainty" to plan ahead through a four-year funding settlement, while a new precept had eased the pressures on specific areas such as adult social care.
"Ministers have committed through a manifesto pledge to further help local authorities control more of what they raise, and we're working closely with the LGA to agree the best way to achieve this," the spokesman said.
Communities Secretary Sajid Javid will use the conference to launch a £2.3 billion fund to pay for infrastructure to support new housing developments.
The Housing Infrastructure Fund, first announced last November, will support the creation of roads, utilities, schools and other facilities.