Furious local government leaders are accusing ministers of a crude political fix to help London mayor Boris Johnson, after establishing that almost every council in the country faces cuts in 2015-16 well above the previously announced 10% – but the Greater London Authority will suffer none.

Analysis by the Conservative-controlled Local Government Association shows cuts nationwide will be nearer to 15%, due to ministers holding back £1bn to distribute in line with policy changes in areas including social care and house building.

By contrast, London will face zero reductions in 2015-16, meaning Johnson will be insulated from the worst effects of budget austerity before the next mayoral election in 2016.

The LGA says that because local authorities have a statutory duty to try to balance their books, they will not be able to rely on possible future payments but will have to cut their cloth according to known income, meaning inevitable losses in front line services. For many councils, the cuts over this five-year parliament will have totalled above 40%.

LGA sources said Tory, Labour and Lib Dem councils had all had to "tear up their financial plans and start again" after discovering the figures were to be even worse than feared.

Sharon Taylor, chair of the LGA's finance panel, said: "Councils have had to go back to the drawing board and are looking again at how they can cope with the cuts. The end result is not going to be pretty. A 10% cut was bad enough, pushing many areas into an unsustainable financial position and threatening to wipe out non-statutory services. The 16% reduction will eat into services most have previously been able to protect.

"Council funding is shrinking at the same time as demand for local services is going up as a result of our ageing population. These unexpected cuts push councils closer to failure. No political party can ignore this problem any longer."

The LGA, which represents 370 councils in England and Wales, found 181 councils now face cuts to their main central government grant of 15% or more, with 69 authorities set to have funding cut by 16%. Just seven face cuts of 10% or less.

Even Tory councillors believe that central government is deliberately forcing cuts on local authorities so that they, rather than national government, are blamed for the effects of austerity.

Hilary Benn, shadow secretary of state for communities and local government, said it was "astonishing that George Osborne and Eric Pickles weren't straight with local government at the time of the spending review announcement about the true impact of these cuts. Only now do we discover what they were really doing."

He added: "Since money is so tight, and the consequences of these cuts on services to the public will be so severe, the government should be devolving as much of the available funding as possible direct to councils rather than keeping it back. Local communities and their elected representatives are in a much better position to make decisions about what the priorities should be rather than out of touch ministers.

"It's also clear that – once again – funding is being unfairly distributed. Many will suspect that the Greater London Authority is getting special protection because Boris Johnson may want to run again as mayor in 2016."

Local government minister Brandon Lewis accused the LGA of being disingenuous, adding that the total amounts allocated had not changed since the chancellor's spending round announcement. "Councils account for a quarter of all public spending and councils are forecast to spend £102bn this year – up on the year before.

"Councils must play their part reducing the deficit left by the last administration and in the recent spending round the government set out a saving of 2.3% for 2015-16 in overall local government spending, including funding from central government, business rates and council tax income. This change is balanced with a progressive package of measures which create a real opportunity to transform local services and help deliver better outcomes for less.

"It is disingenuous of the LGA to suggest there are further budget reductions since the total amounts allocated to local authorities have not changed since the spending round."