The chief executives' body said many members had complained about late payments of sums as great as £500,000 as the end of the financial year approached.
Stephen Bubb, chief executive at Acevo, said some councils were also refusing to fund pay increases for voluntary sector staff, such as social workers, whose pay is tied to local authority rates.
"They have increased the poll tax to give their own staff rises of 2.95 per cent, but they are refusing to put more than 2 per cent extra into contracts for the sector," said Bubb. "It's not political in the sense that it's done by senior officials or policy-makers - it's just the old habit that when you make cuts you pass them on to the voluntary sector.
"It makes a strong action plan from the Government in May all the more important, with references to proper contracting, pricing and distribution of risk."
The Wilf Ward Family Trust, a disability care provider, is owed £138,000 by Leeds City Council. Richard Pacey, chief executive at the trust, said a reorganisation at the council meant no one was taking responsibility for the missed payments.
"It's a bit of a blackmail situation for charities," Pacey said. "But what do we do? Do we turn around and say we won't do it any more? As a charity, it's very difficult for us to do that.
"In certain circumstances, however, we will have to give people notice if the money isn't coming. We can't continually help local authorities balance their budget."
At St Giles Hospice in Lichfield, chief executive Peter Holliday said payments had been later than in previous years. "There has been a marked change," he said. "There is much evidence of difficulty within the NHS, and I've no doubt that this is associated with that.
"We are content to help our statutory sector colleagues on a one-off basis this year, but if we were asked to do the same next year we might get nervous."