The BBC reported the findings after carrying out a survey of 49 councils (employing 256,000 members of staff) and 150 chief executives of borough councils. This means libraries and nurseries could face job cuts as budgets are decimated.
But trade union Unite claims this "scaremongering" will be detrimental to economic recovery.
Gail Cartmail, Unite assistant general secretary for the public sector, said: "These authorities are planning or already implementing cuts to jobs and services in a year when they have received a 4% growth in funding from central government.
"It is a con and scaremongering tactics to make people believe that somehow it is all right to accept that much-cherished local services, such as their local library or nursery, are now somehow ripe to be targeted.
"In a number of cities as many as two thirds of the economically active are employed in the public sector and the impact of such cuts would be devastating to local economies.
"The reason that local government provides such services as roads, libraries, the arts and leisure services, which appear to be top of the list for these cuts, is that there is a long-standing demand for them - they are valued by their local communities."