The party released figures obtained under the Freedom of Information Act showing that one in seven posts are left unfilled.
It also revealed there has been a 30 per cent rise in vacancy rates in England since 2005 with eight local authorities missing at least a third of the required social workers.
But Unison hit out saying more than half of local councils are Tory-run and it is therefore down to the party to take action to fill vacant social worker posts.
Dave Prentis, Unison's head of local government, said: "It's a bit rich for the Tories to start whingeing about the crisis in recruiting and retaining social workers when they run most councils.
"The Tories could pay more to recruit and retain social workers and other key council staff if they had the political will to do so."
In England and Wales the Conservatives run 216 councils, 104 have no overall control, 48 are Labour, 27 are Liberal Democrat and eight independent. The Conservatives also chair the Local Government Association (LGA).
The Conservatives blamed the government for the shortage in social workers, accusing it of allowing excessive bureaucracy and low morale to dominate the profession.
Shadow children's minister Tim Loughton said: "The crisis in social services began well before the tragic death of Baby P and other similar recent cases.
"In failing to take action the Government has created a vicious circle of overstretch and under recruitment. Unsurprisingly, demoralised and exhausted experts are leaving and very few are coming in to fill their shoes."
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