More than 2,000 charities are being forced to close services and sack staff as local authorities slash their funding, or in some cases completely withdraw it, according to research published on Tuesday.

The study – based on 265 freedom-of-information responses from local councils across England and obtained by the union-backed anti-cuts campaign False Economy – reveals the scale of the impact that cuts are having on the charitable sector. Birmingham city council has cut funding to the largest number of charities, with more than 190 organisations losing out, followed by the cross-council organisation London Councils, which has cut funding to 174 groups.

Many charities will see their funding cut by half while others will lose entire budgets. The hardest hit include children's and young-people charities, with more than 380 organisations hit. Another 150 disability, 142 elderly and more than 110 adult care charities are also affected.

The research immediately raised questions about the role of charities as a cornerstone of the government's 'big society'. Brendan Barber, the general secretary of the TUC which sponsors False Economy, said: "The big society is looking more and more like a big con … These deep cuts to voluntary groups across the UK show that government claims that charities can replace direct services currently provided by central or local government are false."

False Economy says its survey shows more than £110m this year will disappear from charities' bottom line although this analysis, the first attempt to map the extent of the cuts in England, does not include major cities such as Leeds and Manchester as well as some large shire counties such as Hampshire or Tory flagship boroughs like Westminster. These councils refused to hand over data on the grounds it would take too long to extract the information.

The final figure is also likely to be far higher given that some large authorities have not yet finalised where the cuts will hit, and only charities or voluntary groups receiving a funding cut of at least 5% are listed in the research. The calculation includes cuts to charity's grants and where they occur some increases to budgets.

Acevo, the Association of Chief Executives of Voluntary Organisations, which represents 2,000 charity leaders in Britain, has warned previously that the sector could lose £750m this year alone if "central and local government passed on cuts proportionately". Another £250m would be lost because of VAT increases and reductions in tax breaks.

Peter Kyle, deputy director of Acevo, said that if ministers' pledges of extra funding, outlined in last month's public services white paper, were to materialise then there would be another £2bn for charities – enough to fill the gap left by the estimated £1bn shaved from their local government grants. "But charities are instead going to the wall because of the cuts and you cannot magic them back into existence again. It's short-sighted and mindless."

Experts also questioned whether the charitable sector could cover for the sharp drop in funding for local government. Tony Travers of the London School of Economics pointed out that local authorities last year had to bear more than £4bn in cuts – amounting to an 8% drop in real terms: "Ministers have created a much bigger challenge in hoping to expand the voluntary and NGO sector in the name of the big society with the size of such cuts."

The government blamed councils for "being short sighted in their approach [and] failing to recognise the importance of the sector". A spokesperson for the Department for Communities & Local Government said: "In their approach to budget setting, the best councils are showing that they understand that a strong, thriving voluntary sector is more important now than ever and could be the key to providing high quality, good value services to their residents. But this is not the case everywhere."

Sir Merrick Cockell, chairman of the Local Government Association, defended its decisions to cut budgets in a time of austerity. "The severity of cuts to council budgets means savings are having to be made across the board, and unfortunately funding to charities, voluntary organisations and community groups is not exempt."

Decisions to reduce financial support to the voluntary sector will never be taken lightly and local authorities have rightly carried out full and frank consultations before reducing funding to groups."ENDS