BACKBENCH city councillors are calling on the authority to ease the pressure on people with multiple debts owed to different departments.
They fear recently-introduced welfare reforms could plunge thousands of households across the city deeper into debt.
As a result of the changes, nearly 25,000 low-income households in Hull are having to pay council tax for the first time.
In addition, nearly 5,000 households are making a contribution to their council rent for the first time because they have been classed as under-occupying properties with spare bedrooms.
Now, a panel of councillors is calling on the council to give more help to people owing money to different sections of the authority.
They want to see a single regular payment system being introduced for people struggling to make multiple instalment payments.
Councillor John Abbott said it was "morally repugnant" to imagine different council departments chasing the same individual for different debts.
"We should not be operating with a silo mentality, where departments are acting independently over issues like this.
"We were told the software is available to integrate computer systems to deliver an integrated debt recovery system. If that's the case, the money needs to be found to make it happen."
The panel spent five months looking at a number of key anti-poverty issues, including finance, fuel and food.
As well as changing the way the council pursues debt, it called on the authority to consider ways of guaranteeing small loans for the Hull and East Yorkshire Credit Union as a way of offering alternatives to high-interest loan deals being offered by payday loan companies.
The panel also backed the credit union's current proposals for a new so-called 'jam jar account' for members to split their account balance into different pots for spending, saving and paying bills.
Panel chairman Councillor Andy Dorton said: "Most citizens of this city are crippled by debt than just about anywhere else.
"It is hard to know the extent of it and the depth of despair of many who are in it. Unless the problem is addressed, we will not alleviate poverty. Unless there is affordable finance and other goods, we will not alleviate poverty.
"Unless we work with and promote our partners in this, we will not eradicate poverty."
He said mindsets need to change over the way people dealt with their finances.
"We may not eradicate poverty but the council can, by a fundamental shift in both its attitude to it and its role in tackling it, enable all of us to make our money go further."
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