The South Yorkshire branch of the Police Federation made the claim after the Government announced a two per cent pay rise for officers but failed to give forces any extra funding.
Police Federation representatives across the country have written to the Government demanding answers over the lack of funding for the pay award.
Zuleika Payne, chairman of the South Yorkshire branch, said: “Our members are angry and forces have been put in an impossible situation. We feel the government has not been truthful and honest about the pay award given to officers, and that is insulting.
“The two per cent awarded has to come from existing policing budgets which means forces may have to choose between officer numbers and public safety. That cannot be right.”
The letter demands answers on a range of issues, asking for the truth about crime figures, police numbers and claims of ‘extra’ officers.
Ms Payne added: “Crime is not falling, it’s on the up and cyber crime has exploded. Officers are having to do more and more and cries of extra police officers being on patrol are not ‘extra’ police officers. They are the same officers doing longer hours, being called back in when they are off or being given extra responsibilities. It is all smoke and mirrors and double standards.
“The public have been fantastic at giving us support but they deserve better. Officers give all to become police officers but they are broken; unable to cope with the mental and physical demands placed upon them by having to work in depleted environments. This cannot be right or fair on anyone - let alone the public.
“We don’t want meaningless platitudes. We want a properly funded and well-resourced police service. The public rightly want and expect this, which is why we have called for answers.”
Last month, South Yorkshire's Chief Constable Stephen Watson warned that the pay rise for police officers could mean cuts need to be made.
He said he is 'pleased' the Government has awarded police officers a pay increase to 'reflect the challenging work that they do' but pointed out that no extra cash has been awarded to forces to pay for the salary increases.
The pay rise will add an extra £1 million onto his force's wage bill.
South Yorkshire's Police and crime Commissioner, Dr Alan Billings, said if reserves need to be used to pay for the salary increase, it was a 'potentially dangerous path' to take.