Ten households a day are appealing for emergency financial help to pay for food as they adjust to changes to the benefits system.
Figures released by Bath and North East Somerset Council show the scale of demand for a share of its £249,260 emergency assistance social fund.
The fund provides shopping vouchers for supermarkets to enable people to pay for food, prescriptions and essentials including nappies, as well as helping people pay fuel bills, council tax and buy items such as ovens and fridges.
The council has handed out just over £8,062 in the last two months – approving half of all applications since taking responsibility for such crisis funding from the Government.
B&NES' new scheme – which uses Whitehall cash – is split into two.
Part one is targeted at supporting low income residents who cannot meet expenses, such as food, out of their wages.
Part two provides emergency assistance at times of desperate need, such as flooding, fire or bereavement.
However, staff at Bath's Citizens Advice Bureau, who are helping up to five people a day with food bank vouchers or fuel meter payments, say the council's scheme is not suitable for everyone.
Operations manager, Gill Whitehead, said: "We are often approached by people who have no money at all for food or topping up their fuel meters. This may be because of problems with benefit payments, bank accounts or debt issues which have not been addressed.
"Many of these people would previously have been able to apply for crisis loans.
"However, the new local authority scheme is much more limited in scope. To qualify for the full range of assistance clients need to be either in receipt of a very small range of disability benefits or have children under five.
"This excludes people with older children or less severe illnesses and disabilities, as well as people who are unemployed and seeking work, single homeless who are on the very lowest benefit incomes."
She added national changes to housing benefit and council tax support were making many household budgets unmanageable.
She said: "Our advisers are finding it almost impossible to balance many clients' budgets when advising them on debts, particularly when they are affected by more than one of the changes."
Social landlord Curo agreed that households in the city were struggling to cope with changes to the benefits system with rising concern that people might turn to payday or doorstep lenders renowned for high interest rates.
In April households were hit with changes to council tax and disability living allowance, a £500-a-week cap on benefits paid to families, as well as the bedroom tax, which targeted working age households with spare rooms.
Those with an extra bedroom have been told they have to move to a smaller place or have some of their housing benefit taken away.
Head of service development at Curo, David Clarke, said the organisation had been inundated with appeals for help over the so-called bedroom tax.
"People are thinking about how they are going to afford things. People are worried about ultimately losing their home if they can't afford to pay it."