CITY council leader Steve Brady says the authority has been put under unprecedented pressure because of budget cuts.
Calling on ministers to resist making further reductions in local government funding, he said losing about a third of its budget since 2010 had created enormous pressures on staff and services.
Chancellor George Osborne is due to unveil the results of his latest spending review later this month, with further cuts to council funding being widely forecast.
The Local Government Association (LGA) recently warned that some councils will soon start failing their communities by being unable to deliver statutory services if the cuts continue.
According to the LGA, up to 86 councils are at risk of financial meltdown.
Cllr Brady said: "No one can say this past year hasn't been challenging for this council.
"I can't remember such devastation that has been caused by the financial crisis and the effects it has had, particularly on local government.
"The LGA has recently said that we are very near a tipping point, that councils cannot carry on making deep cuts when they are so many problems with social care and other aspects of what we need to do to look after the citizens of Hull.
"Seventy-four per cent of the worst-hit councils are in the north of England and since Councillor Carl Minns was leader of this council, there have been twice the level of cuts to this city compared with those he announced in 2010.
"£228 per head has been wiped off the finances of this council. On top of that we have had the bedroom tax, which is causing real pain in this city.
"When I hear people on the TV and radio saying there are simple solutions to the effects of these cuts, I just remind people of the effects of these simple solutions, because what happened was 1,000 jobs were wiped out at this council in four weeks under the previous leader.
"That wasn't a well thought- through plan.
"Certainly, there are still people in this authority losing their jobs – people who have worked tirelessly for the people of this city who, through no fault of their own, are seeing their employment in jeopardy.
"We are trying to do it and trying to alleviate as many of the problems facing our employees and the people of the city."
LGA chairman Sir Merrick Cockell said: "Local government has so far borne the brunt of cuts to public spending. If the Government pursues the same policy again, local services will suffer to the point where many councils start failing their communities."
