Cut to the "formula grant" for councils in London are at a level not "seen in a generation", the body which represents the 32 boroughs has said.
The comments come after Communities Secretary Eric Pickles announced a 9.9% cut in government funding in 2011/12, followed by a 7.3% fall in 2012/13.
London Councils chairman Jules Pipe said "no combination" of cuts would be able to protect services.
East Ham MP Stephen Timms said deprived boroughs suffer the "biggest losses".
The fall in formula grant, which is the main grant councils receive from the government, means local authorities could see a cut in their spending power of 4.4% next year and a drop of more than 8.9% for any of the next three years.
The formula grant excludes funding for education, public health, and transport.
Mr Pickles told MPs: "This will be a progressive settlement, ensuring fairness between different parts of the country."
Jules Pipe, who is also the mayor of Hackney, said: "London Councils called for the frontloading of these cuts to be eased.
"The government has taken a step in this direction, but frontloading remains at the heart of the settlement - the cut in April 2011 is almost 50% higher than in year two.
"London's councils are already planning for improved efficiency, shared services and new approaches to service delivery.
"The scale of these reductions is so large that no combination of these is sufficient to protect the services that Londoners expect to be funded."
Questioning Mr Pickles, Labour's Mr Timms said: "Given what you have said about fairness, 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 disadvantage are the greatest."
Mr Pickles said the poorest boroughs in London were not as severely affected as they otherwise would have been.
Labour MP for Lewisham Deptford, Joan Ruddock, said: "This will be devastating to my deprived constituency and borough of Lewisham.
"With 40% of the budget being spent on elderly and children's care, can you not see that this will mean draconian cuts in everything else?:"
The cuts follow the coalition government's spending review plan, unveiled in October, to reduce funding by 28% over four years to reduce Britain's budget deficit.