Members of the public are misusing the 999 system by calling it instead of the non-emergency 101 police number to report minor incidents because they have run out of credit on their mobile phone.
The trend identified by the South Yorkshire branch of the Police Federation is one of a number of issues said to be increasing pressure on the county force's over-stretched employees
Zuleika Payne, chair of the local branch, raised the number of non-police matters being reported to the South Yorkshire Police call centre and of callers making appointments for help and then not turning up.
She spoke in response to the news, revealed in The Yorkshire Post on Saturday, that Chief Constable Stephen Watson plans to move between 300 and 500 officers into neighbourhood policing roles.
He said officers would be transferred into local problem-solving positions from 24/7 response teams after years where the force had become too reactive.
Ms Payne said it "remains to be seen" how this model of policing would be funded, because of the lack of officers available. She said the welfare of officers was an "increasing concern" and that they were often unable to take meal breaks or secure annual leave.
She said: "Right across the board from response officers, to CID, Specialist Operations Units and Public Protection units, all areas are under resourced."
The force, which gets an average of more than 600 999 calls a day, and 1,700 to its 101 service, has faced heavy criticism for the performance of its Atlas Court communications centre in Sheffield.
It is looking at ways to reduce the amount of time callers spend on hold when they call the non-emergency number and bringing in extra staff to answer calls.
Ms Payne said: "Frustratingly, many incidents coming into the call centre are not necessarily matters for the police to deal with.
"Coupled with instances of misuse of the 999 system when callers have simply run out of credit on their mobile phone.
"Hence the force is also looking at ways as to how these issues can be addressed in order to maintain the efficient and appropriate use of our officers.
"There are a number of appointments which callers fail to keep having requested police assistance, which again has a negative impact on our service delivery.
"If we are going to achieve an effective and efficient way of working all these concerns have to be addressed."
Calls to South Yorkshire Police increased by three per cent last year, with more than 40 per cent relating to public safety concerns, such as a missing person, a domestic incident, or someone collapsing in suspicious circumstances.
It costs 15 pence to call 101, no matter how long the call or what time of day, whereas 999 is free to call, even from mobiles with no credit.