Ministers stand accused of using double accounting to mask £200m of cuts to money used for libraries, care of the elderly and protecting children.
It has emerged that millions of pounds included in council budgets for the coming year is already being spent by the NHS.
The money, known as the Better Care Fund, is supposed to help Yorkshire councils deliver joined up services with the health service.
But council leaders say the reality is the money is also being counted in the NHS budget and has already been allocated to support health services.
They claim the Better Care Fund is actually a sleight of hand to make cuts to their budgets for services such as social care and waste collection look less severe.
Leeds City Council is planning to make savings of £50m in the year ahead and cut 200 jobs while also proposing to raise council tax by 1.99 per cent.
Council leader Keith Wakefield said: “We are facing one of our biggest ever challenges in health and social care which we are making progress with and which has been recognised nationally.
“This is a deception on the people of Leeds and on Parliament, it is outrageous.”
The Government has angered councils by using a formula known as “spending power” to assess their finances rather than setting out cuts in grants.
Figures produced by SIGOMA, a body representing largely urban authorities including 10 in Yorkshire, show that even on the Government’s own figures the region’s councils have seen their spending power cut by £113m for the coming year.
However, when Better Care Fund cash is stripped out that rises to more than £300m.
And many council leaders say the reality of the cuts is larger still because the spending power formula distorts the picture in many other ways.
Barnsley Council leader and SIGOMA chairman Sir Steve Houghton said: “The Government has used the spending power measure to mask what is happening in terms of cuts across local government.
“This is another example, where money has been taken from clinical commissioning groups and used in this calculation when there’s no new money.
“Spending power doesn’t give a transparent picture of what’s really happening and in my view that is why it is being used - to cover the fact that not only are the cuts very severe but very disproportionate across the county.
“Areas of deprivation have taken the brunt of the cuts.”
Sheffield MP Clive Betts has asked the UK Statistics Authority to intervene and force Ministers to be clear about the reductions in funding going to councils.
Speaking in the Commons, he described the way councils are funded as “fundamentally broken” and called for a “fundamental review” of local government finance.
Mr Betts said it was time to give more powers to local authorities, to consider giving them more freedom to raise money and for councils to receive money in a way that reflects deprivation levels in their areas.
A spokeswoman for the Department of Communities and Local Government said the Better Care Fund was designed to give councils access to money they had not previously been able to tap into in order to work with the health service more closely.
North Yorkshire, Bradford, Wakefield and York are among the other Yorkshire councils which have signalled council taxes will rise in the coming year.