West Lindsey council let up to four employees go last year, figures show.
The Association of Local Authority Chief Executives and Senior Managers said job losses will continue across England because the Government does not see local councils as a priority.
Figures from the Ministry of Housing, Communities and Local Government show between one and four exit packages were awarded by West Lindsey District Council in 2020-21 – though the total cost of the payments is unavailable, to maintain confidentiality.
Up to four staff were also laid off the previous year.
The total value of exit packages nationally more than halved from £544 million in 2016-17 to £252 million last year in real terms.
Ian Miller, honorary secretary of the ALACE, said: "The higher spend between 2014 and 2017 reflects that councils were making very significant reductions in their workforce at that time as a result of the Government's austerity programme which has cut funding for local government since 2010.
"Job cuts will continue because local government has not been a priority for this or previous governments."
He added that councils aim to protect frontline services, and that workforce reductions slowed in 2020-21 because the focus was on responding to the pandemic.
Since 2014-15, the average cost of exit payments has risen by 31% for senior employees – when adjusted for inflation – and 15% for those below this level.
Mr Miller said costs for older employees tend to be higher as the local government pension scheme requires immediate payment of pension rights where someone over 55 is made redundant, or let go to make the council run more efficiently.
The figures were published as part of the Government's research into ending "excessively high" exit payments in the public sector.
Legislation passed last year – which capped payments at £95,000 – was revoked in February after the Government admitted it may have had "unintended consequences" for the lowest paid workers.
Mr Miller said the figures show there is no need for a cap when the average exit payment is just £26,703.
The Local Government Association said its survey of local authorities indicated that many planned redundancies in 2020 and 2021 for several reasons, including funding shortages and local government reorganisation.
It said council restructures tend to be focused on removing senior posts, which means older, longer-serving and higher paid staff are often the ones affected – and these workers are also more likely to volunteer for redundancy.
An LGA spokesman said: "Councils are required to ensure termination payments are fair, proportionate, lawful and provide value for money for the taxpayer."
The MHCLG said councils are best placed to make decisions, but that the Government is still committed to tackling excessive exit payments.
An MHCLG spokeswoman added: “Severance pay is the responsibility of individual councils and we urge them to ensure that payments reflect value for money to the taxpayers who fund them.”