The umbrella body says that councils for voluntary service and volunteer centres in several areas could be forced to close or severely curtail their services.
NACVS director of information and policy Neil Cleeveley said: "Our members provide vital support services to local groups. Funding for these organisations is under pressure in many areas. It is worrying that some services are threatened. All this is at a time when the Government expects local infrastructure to be at the heart of things."
A survey of NACVS members has found that only 16 per cent of local authorities will provide a real-terms increase for infrastructure services for the next financial year.
Among Primary Care Trusts, only a quarter are budgeting for an above-inflation rise for voluntary sector infrastructure services.
NACVS is warning that councils for voluntary service could close in Castle Point in Essex, Chiltern and South Buckinghamshire, and Malvern. Ipswich Volunteer Centre is also under threat.
Cleeveley said that NACVS welcomed the Government's ChangeUp investment in voluntary sector infrastructure, but also believed that local authorities have a responsibility to fund the sector at a local level.
"Local Area Agreements will require a well-developed infrastructure, and local authorities are missing the point," he said. "Many seem to believe that ChangeUp will absolve them of their responsibilities. Authorities can't cut year on year without affecting services and support."
In 2002 and 2003, then Home Secretary David Blunkett authorised emergency funding of £500,000 to save local councils for voluntary service and volunteer bureaux threatened with closure because of cuts in council funding. But with the Home Office's £150m ChangeUp programme now in place, NACVS is expecting no more assistance from central government.
News of local authorities' budgetary retrenchment comes as NACVS chief executive Kevin Curley prepares to make a strong attack on their record of supporting the voluntary sector at next month's CharityFair.
He will urge charities to take a more hardline approach with recalcitrant local councils. "We should pursue the offending local authorities with every stick available to us," he will say.