Rugby Borough Council has written to nearly 1,000 residents currently claiming Council Tax Reduction or Housing Benefit to raise awareness of the support on offer - but has urged all residents worried about the winter bills to check eligibility for help.
Recent research revealed £23 billion of benefits goes unclaimed every year in the UK - with 1.1 million pensioners missing out on at least £3,778 a year in Attendance Allowance and 1.4 million failing to claim an average of £5,800 a year in Universal Credit.
Other benefits thousands of people fail to claim include Pension Credit, Carer's Allowance and Council Tax Reduction.
To support residents, the council launched a new benefits calculator on its website this week, making it quick and easy to check which benefits you're entitled to.
And Cllr Claire Edwards, Rugby Borough Council portfolio holder for communities and homes, regulation and safety, said the ten minutes it takes to complete the benefits calculator could be time well spent.
"We know the cost of living can be particularly challenging during winter, with increased energy bills and Christmas, so now's the time to make sure you're not missing out on state benefits which, in turn, can often mean you're eligible for other financial support," Cllr Edwards said.
"We understand the stigma many people feel about claiming benefits, but all of us contribute money to our social security system so it's there to support us when we need it, just like the NHS.
"Nobody should feel embarrassment or shame for reaching out for support - it's money you have earned and you're entitled to.
"You may qualify for help with your energy and water bills or be eligible for social tariffs offered by your phone or broadband providers - there's a lot of support on offer and we don't want residents to miss out," Cllr Edwards added.
"We have published a 'winter support' section on the council's website, alongside the new benefits calculator, and I'd encourage anyone worrying about winter bills to take the time to check you're receiving all the support you qualify for."
For more information about the winter support on offer, visit www.rugby.gov.uk/wintersupport
The benefits calculator can be found at www.rugby.gov.uk/calculator