England's communities are being "short-changed" by £4.1bn a year under the model used to allocate central government funding across the UK, the Local Government Association has said.
This money needed to be "repatriated", demanded the LGA, which represents councils in England and Wales.
It should then be used to address the "crisis engulfing adult social care", the body argued.
Council funding is always desperately complicated. Throw in the added dimension of devolution, and the upcoming Scottish referendum: you've got a tangle that the finest financial and political minds will struggle to make sense of.
Criticised by the English for being unfair, by the Welsh for doing no favours to Wales and by the Scots for institutionalising Westminster hand-outs, the Barnett formula, it seems, satisfies no-one.
The model used to determine how central government funds are divided up is called the Barnett formula, after former Chief Secretary to the Treasury Lord Barnett.
LGA chairman Sir Merrick Cockell said: "The Barnett formula has passed its use-by date. It is an historic relic from a time when the government stopped people taking more than £50 on a holiday abroad.
"What was only ever intended as a stop-gap solution has now become a major problem which is short-changing English communities and underfunding their public services by £4.1bn a year."
He argued that a "fair and equitable distribution of public money" across the UK was now needed.
"The crisis engulfing adult social care demands a shift to a needs-based formula for distributing funding," Sir Merrick continued.
"Our ageing population means that there is an enormous increase in demand for council-run adult social services, which must be met to ensure people retain dignity as they get older.
"The major political parties should all make the introduction of a needs-based formula a cornerstone of their pre-election manifestos and the chancellor should look to lay the groundwork for it in his Autumn Statement."
Debate on the Barnett formula goes to the heart of the debate on Scottish independence.
Nationalists argue Scotland gets a raw deal from the Barnett formula, but some unionists believe the formula needs changing to give Scotland more financial powers.
Welsh ministers advocate a new needs-based formula, taking into account such things as the age of the population and poverty levels.
The Northern Ireland Executive says it is difficult to assess whether the level of funding it receives under the formula is fair.
The LGA said that England's ageing population was increasing demand for council-run adult social care services by 3% each year, meaning councils would have to find an extra £400m per annum.
Meanwhile councils' central funding was "being cut by 43%", the LGA claimed, "placing social services under enormous strain and leading to reductions in services and a tightening of eligibility criteria".
The UK government disputes the LGA's analysis, arguing that central government funding cuts are offset by increases in "spending power".
This term encompasses a number of factors, including the retention by councils of a higher proportion of taxes levied on local businesses, and "bonus" funds for councils that approve the construction of new homes.