A leading charity figure and key supporter of David Cameron's "big society" project warns that massive public spending cuts could doom the prime minister's main social policy initiative to failure and become a Hurricane Katrina moment for the government.

As Ed Miliband accuses the government of adopting a "forbidding and unheeding" approach to reducing Britain's fiscal deficit, David Robinson declares that a barrage of unsustainable cuts will damage Britain's poorest neighbourhoods.

In an open letter to Cameron, the co-founder of the Community Links charity warns that vital local voluntary organisations will be wiped out.

Robinson, whose charity has been described by Cameron as "one of Britain's most inspiring community organisations", writes: "Forcing an unsustainable pace on a barrage of uncoordinated cuts that hit the poorest hardest is not an act of God. Why let it be your Katrina?"

The attack on the PM comes as Miliband launches one of his strongest attacks on the coalition's plans to eliminate the structural deficit over the course of this parliament, in contrast to the Labour proposal to halve it over four years. In his new year message, the Labour leader says: "Here at home, 2011 will be a year of consequences for Britain. Consequences that will be felt by hardworking families across the country. Consequences of the decision taken to reduce the deficit at what I believe to be an irresponsible pace and scale.

"Many people feel powerless in the face of these decisions that will affect their lives, families and communities. The political forces in Whitehall which have made these choices appear forbidding and unheeding."

There were also warnings from trade unionists of possible strike action. Mark Serwotka, the leader of the Public and Commercial Services Union, told the Times: "Strikes are inevitable. We are looking at the spring. The more of us that stand together against the cuts, the more problems we can create.

"Unless you look like you want a fight, they won't negotiate. The government has to see we are serious."

Robinson gives a practical example of the impact of the cuts when he warns that deprived areas face a "double whammy" of increasing unemployment and cuts to services. He says that Community Links, based in east London, faces an uncertain future because of the government's changes to legal aid and welfare-to-work funding. "Charities like us are surely the bedrock of the big society, and we are wobbling."

Robinson, who regards himself as a "critical friend" of Cameron, praises his "big-hearted vision" and commitment to big society principles, but warns that without a big injection of cash, Cameron is in danger of losing any credibility he has a compassionate politician.

His comments reflect widespread nervousness and anger in UK charities at the speed and unco-ordinated nature of the cuts. As councils, NHS primary care trusts and Whitehall departments attempt to deliver the massive budget cuts from next March, recent surveys suggest huge numbers of charities face potentially calamitous losses of grants, contracts and infrastructure support. Examples in the last fortnight include:

• About 2,500 charities that provide welfare services in Greater Manchester – around a quarter of all voluntary groups in the area – could go bust because of the cuts, according to estimates by the Greater Manchester Centre for Voluntary Organisation.

• A quarter of charities in the north-east of England which depend at least partially on public funding will go bust in the next 12 months, according to research by Voluntary Organisations Network North East. It says that while demand for services has rocketed, 64% of charities surveyed say they will be forced to close services.

• A third of charities nationally that receive state cash say they will have to reduce the level of services they provide, while over a quarter expect to make staff redundant, a survey by the Charity Finance Directors Group, consultants PWC and the Institute of Fundraising found.

The charity thinktank New Philanthropy Capital recently estimated that the voluntary sector's income from state sources could shrink by between £3bn and £5bn as a result of the cuts.

Nearly a quarter of all charities get cash from the government, and 13% rely on state funding for more than half of their income.

Robinson calls for an urgent assessment of the cuts. He tells Cameron: "I'm not asking you to renege on policy pledges, but give us more time … Allow us to draw breath or you will kill off the agencies you need to build the society you seek."

Although the government is preparing to launch a big society bank to lend to charities and social enterprises next spring, Robinson argues it is undercapitalised, and will not solve the immediate funding crisis. "Our most desperate need now is to maintain those services for the most vulnerable which will never be self-sustaining.

"It is these that are least likely to survive and it is the public funding of this provision that marks out our economy as that of a civilised and compassionate society."

He says the rapid withdrawal of resources as a result of cuts will cause a build-up of unmet social need among the most disadvantaged citizens that will in turn create an expensive long-term problem for the state.

Community Links, which was set up in a back room in East Ham by Robinson, Kevin Jenkins and a group of volunteers, has grown into the UK's biggest and most admired community organisation, providing a range of welfare services, from housing and debt advice to employment support and children's centres and youth clubs to more than 30,000 East End residents. Its latest accounts show it has an income of £9m, of which the lion's share comes from central or local government sources.