Budgets for Sheffield and any other council are set in Westminster, centrally, by the government.
The last 10 years has seen real time cuts to the budget year on year, I believe Sheffield is one of many councils who's welfare spending outweighs its direct taxation and so realises on extra money from the government just to keep its head above water, things like this will be happening all over the country as local authorities scramble to squeeze every last penny out of the pound.
The fact that no meaningful infrastructure has been build or any other attempt at some decent economic stimulus in the north in the last god knows how many years, coupled with the rising demand and cost of health care means welfare spending is only going one way and that's up, its a self for filling prophesy we should have been borrowing and investing more to drag ourselves out of the red and reduce reliance on the state, especially while world interest rates have been at histrionic lows.
Now all that's going to start slowly changing as the cost of borrowing increases due to the UK raising % raters and strengthening the pound to allow us to be somewhat competitive when importing goods, seen as we import virtually everything, we will find ourselves unable to break the cycle.
But Dan and Dave at the Conservative HQ know most people will just blame their local councils for everything.