Bath and North East Somerset was among the areas with the most secure access to healthy food, new figures show.
But the figures come as the Trussell Trust says more people across the UK used food banks in the six months to September than ever before.
Campaign group Feeding Britain said a strategy to ensure everyone can afford and access the food they need is desperately required.
The latest Office for Health, Improvement and Disparities figures show 4% of Bath and North East Somerset residents (7,611 people) suffered from food insecurity in 2021.
Food insecurity is when people do not have consistent access to enough food that is varied, culturally appropriate, and can sustain an active and healthy lifestyle.
Andrew Forsey, national director of Feeding Britain, said Prime Minister Rishi Sunak must publish a strategy to ensure people can afford and access healthy food.
Mr Forsey added that food clubs in Feeding Britain's network "have never seen so many people", including working families, seeking help with food.
Rachel Bull, head of policy and research at the Trussell Trust, said: "Food insecurity is a deeply concerning issue that spans the whole of the UK. We live in one of the wealthiest countries in the world, and yet what these statistics show is that hundreds of thousands of people in the UK are going without the essentials we all need to get by.
"We are urging the UK government to create an 'Essentials Guarantee' by changing the law to make sure the standard rate of Universal Credit always, at a minimum, provides enough to the cover cost of essentials such as food, utilities, and vital household goods."
Trussell Trust figures show 1.3 million food parcels were handed out across the UK in the six months to September – a 33% increase on the same period in 2021, and the highest number on record.
Of them, 3,700 were given out in Bath and North East Somerset – up from 3,159 in the six months to September 2021.
A Government spokesperson said it recognises the pressures of the cost-of-living crisis and is "committed to eradicating poverty".
They added: "We have uprated benefits by 10.1%, as well as making an unprecedented increase to the National Living Wage this month. This is on top of changes already made to Universal Credit, which mean claimants can keep more of their hard-earned money.
"We are also providing record levels of direct financial support for the most vulnerable – £1,200 last year and a further £1,350 in 2023-24 – while the Household Support Fund is helping people with essential costs."