North Somerset Council increased its spending on making staff redundant last year, new figures show.
The amount spent by councils across England making staff redundant rose for the first time in six years.
The Local Government Association said councils are facing "significant financial pressures", with the number of employees falling over the last decade.
It said councils require adequate funding and long-term certainty to meet rising costs and avoid more redundancies in the future.
Ministry of Housing, Communities and Local Government figures show around 10 people were made redundant by North Somerset Council in 2023-24.
This cost the council £60,000, at an average of £12,000 per redundancy package.
The number of redundancies is rounded to the nearest 10, and figures for 2022-23 were suppressed to protect people's identities.
Nationally, councils spent just under £200 million on redundancies in the year to March – up from £183 million and the first rise since 2016-17.
An LGA spokesperson said: "The number of people working in local government has reduced in size over the last decade as councils continue to face significant financial pressures.
"In this context, councils make decisions based on their contractual and legal responsibilities when determining the level of severance or settlement payments made to their employees.
"Councils need adequate funding and longer-term certainty to meet rising costs and demand pressures and avoid more redundancies.
"This will also prevent exacerbating an already acute capacity crisis in some areas, with more than nine in 10 councils experiencing staff recruitment and retention difficulties."
The figures also showed a record 380 senior employees were made redundant last year, costing councils £29.7 million, the highest figure since 2018-19.
Council finances have been significantly strained recently, with six councils effectively filing for bankruptcy since 2021. There had been just three between 2000 and 2018.
An LGA survey following last year's Autumn Statement showed almost one in five council leaders said they would likely face bankruptcy in the next two years.
In a speech at the LGA forum, Deputy Prime Minister Angela Rayner said Labour will "end the Dragons' Den approach", in which local authorities bid for funding.
Ms Rayner said: "I know the biggest crisis facing local government is financial. I won’t shy away from that. Demand for services is up, and so are your costs.
"But it doesn’t have to be like this. You told me you need more stability and certainty to plan for the long term, and we will provide this through long-term integrated funding settlements.
"We will end the Dragons' Den approach, as I see it, of the bidding wars between local authorities and instead show you some respect with long-term funding giving you the flexibility to spend it where it is needed."