Local government leaders say English councils face a 12.1% cut in their core central government funding next year.
The Local Government Association has said the settlement for 2011-12 is the toughest "in living memory" and will "inevitably" mean cuts in services.
Communities Secretary Eric Pickles said the average cut in councils' "spending power" - which includes other income like council tax - will be 4.4%.
Labour says the poorest neighbourhoods will be "hardest hit" by the cuts.
Mr Pickles told MPs on Monday that councils' "spending power" for 2011-12 would be cut by 4.4% on average. "Spending power" takes into account both the core "formula grant" which councils get from central government and other income - council tax and other grants.
Some councils rely more on the central grant because they get less in council tax - but the government said no council would face cuts of more than 8.9%, because the worst hit would receive money from an £85m "transition grant" to bring the reduction back to 8.9%
Overall the average reduction in the "formula grant" - made up of business rates, the revenue support grant and Home Office money for police authorities - was 9.9%.
But the LGA, which represents councils in England and Wales, said once the police grant was excluded, central government funding for council services was being cut by 12.1%, from £28.3bn to £24.9bn.
Total funding for local government - including the £38bn schools grants, PFI additional funding and police grants - will fall by 2.7% in 2011-12 to £73.6bn, when compared with 2010-11, the LGA says.
The LGA says it faces rising costs in areas like social care, child protection, waste management and flood defence.
LGA Chairman Baroness Eaton said a £6.5bn funding shortfall over the next year meant cuts to services were "inevitable".
"This is the toughest local government finance settlement in living memory," she said.
"The government has recognised the impact the cuts will have on those areas of the country that rely most heavily on the public sector and has provided a limited amount of new money to help those areas cope.
"However, it still remains the case that the cuts are frontloaded rather than spread evenly across the four years. Councils now face incredibly tough choices about the services they continue to provide and those they will have to cut.
The government says it has taken steps to protect the poorest areas which rely most heavily on public sector services.
Mr Pickles announced on Monday that the "formula grant" from Whitehall would be reduced by 9.9% in 2011/2012 and by 7.3% in 2012/2013 - as part of a policy to cut central funding to local authorities by 28% over four years.
Authorities facing the biggest cuts in their "spending power" - which also includes other grants and council income - include Great Yarmouth, which sees a 26% cut in 2011-12 and Barrow-in-Furness, which sees a 24% cut.
But any authority facing cuts of more than 8.9% will receive a "transition grant" - effectively capping the cut at 8.9%. However the original cut will be used as the baseline for 2012-13 figures.
Mr Pickles said he had given the Local Government Association "what they asked for. I have made sure that no authority will face more than an 8.9% reduction in spending power for either 2011 or 2012/13".
He said it would be a "progressive and fair" settlement with more money channelled to those parts of England in most need.
Mr Pickles said he had sought to insulate areas which most heavily depend on central government funding by creating four separate grant bands for councils, setting different limits for their reductions and protecting councils against the sharper grant reductions.
He said that £650m would be set aside so every council could freeze council tax without hitting local services. The government would provide those who froze council tax with the equivalent of a 2.5% increase in funding.
To help protect front-line budgets, £200m would be provided to help councils modernise and cut back office costs, Mr Pickles said.
But Labour's Stephen Timms said the most disadvantaged communities would be hit hardest. He asked: "Why is it, looking through the list of the London borough graph changes, that the biggest losses in absolute terms and in percentage terms are in local authorities where the levels of disadvantaged are the greatest?"
And Shadow Communities Secretary Caroline Flint said: "All Eric Pickles' warm words about transitional funds can't disguise the truth - the poorest neighbourhoods will be hardest hit while the better off will do best as a result of the choices the coalition government are making."