Members of the Public and Commercial Services union backed walkouts by 61% and other forms of industrial action by four to one. Turnout was 28%.
The Government is facing a strike by civil servants after they voted in favour of industrial action over pay, pensions and working conditions.
The union's leadership will now discuss a programme of strikes and protests, with a decision expected on Wednesday. The ballot result raises the threat of industrial action by Government employees at around the time of the Budget later this month.
The union said that since the onset of the recession in 2008, the real value of wages in the public and private sectors had fallen by 7%. Median pay in the civil service was 4.4% lower than similar jobs in private firms, rising to 10% for some grades.
PCS general secretary Mark Serwotka said: "Civil and public servants are working harder than ever to provide the services we all rely on but, instead of rewarding them, the Government is cutting their pay, raiding their pensions and trying to rip up their basic working conditions.
"We said more than two years ago that austerity wouldn't work and we have been proved right. Under this Tory-led Government, our economy has flatlined, we are heading for a triple-dip recession and the Chancellor has lost his prized AAA credit rating. We urgently need to invest our way out of recession, with an end to the economically disastrous pay freeze and job cuts and with a serious clampdown on tax avoidance and evasion."
The union has called for a 5% pay rise for civil servants and is campaigning against plans to change terms and conditions. PCS officials said the Government had refused to negotiate on issues affecting civil servants.
On the 28% turnout figure, a PCS spokesman said: "No one wants to see low turnouts but Government ministers and their supporters are content that police and crime commissioners have a mandate on a 15% turnout, so it would be rank hypocrisy for them to say otherwise about our ballot."
A Cabinet Office spokesman said: "It is disappointing that yet again the PCS insist on pushing for futile action which benefits no one, and damages the services they deliver to the public. The result from today's ballot shows that the PCS leadership couldn't even convince large swathes of its own membership of the benefits of walkouts. The Government took the tough decision to freeze public sector pay for two years, while protecting those earning under £21,000 by increasing their pay by at least £250 per year. Pay restraint has helped to protect jobs in the public sector and support high quality public services.
"In March 2012 we set out our final proposed agreements on pension reform following more than a year of intensive discussions with trades unions. These reforms will ensure that public sector pensions will remain among the very best available and that they can be sustained for future generations. Because we want to attract the best staff we will remain an employer with good terms and conditions, as we have always been. However, while there has been significant recent change in pay and pensions, there are other terms and conditions that have not been updated. We will address this and ensure a modern employment offer is available to all."