Most of the food comes from food manufacturers before it reaches the supermarket shelves, and may have been poorly labelled, or over-ordered by the retailer, while other goods are donated direct from the supermarkets.
If the food had not been re-distributed via Company Shop it is likely that it would have ended up in anaerobic digestion for waste management and fuel production, as animal feed, or in landfill.
Company Shop director of environment and social affairs Sarah Dunwell said that 500 people will be given membership for six months to test whether the social supermarket idea works.
Those behind the scheme then hope to launch a further 20 branches across the country next year, including six in London.
Ms Dunwell said: "We are aiming to fill a gap between food banks and mainstream retail. Lots of families are not in an emergency situation but are on the cusp of food poverty.
"It is for anyone who is claiming any of a list of benefits. It is not just about the long-term unemployed but really hard-working families who are struggling.
"It's more than about just cheap food.
"We offer a fully package of support with a cafe, a cookery school, support for people who need advice on payday lending, alcohol support and domestic violence among other things."
The supermarket, which opened this morning, will not sell alcohol or tobacco.
Ms Dunwell said: 'We'll have staples such as sugar, pasta and rice but also more expensive goods such as French cheeses, ready-made lasagne and desserts and household products.
"This is not cheap food for the poor, it will bring a huge range of foods.
"It takes stuff that will not make it to supermarket shelves and uses it to feed people who need it most.
"While we have people in the UK going hungry it is wrong such foods should be thrown away."
Members will be assessed at the end of six months with the aim being that they no longer need the social supermarket, and as well as access to cheaper goods will be offered tailored support programmes including debt advice, cookery skills, home budgeting and CV writing.
Ms Dunwell said: "With many families facing tough times in Barnsley, Company Shop wanted to do more to match surplus stock with people who really need it.
"Industry surplus is hard to avoid, but what Community Shop shows is that if we all work together we can make sure that surplus food delivers lasting social good."
Leader of Barnsley Council, Sir Steve Houghton said: "The new store will be a great asset for local residents enabling them to access a range of high quality low cost food as well as a place where they can access local services."
Bosses at major supermarkets have also praised the new scheme.
Asda president and chief executive Andy Clarke said: "Despite our continued investment in lowering the price of every day essentials, sadly there are still people in society living in food poverty.
"As one of the UK's largest retailers, we have a crucial part to play in supporting those families who need us at difficult times through Community Shop."
Martyn Jones, group corporate services director at Morrisons, said: "Morrisons is delighted to support Community Shop for the step change in food redistribution that it will offer.
"What's so appealing about this project is that it provides a new, readily identifiable store outlet that can reach people who really need some support."
Steve Murrells, chief executive at The Co-operative Group, said: "Community Shops are an innovative way of tackling the increasing social problem of food poverty, and this project fits well with The Co-operative's values.
"We are working with Company Shop to see how we can develop our existing relationship to support this project."
Chair of the London Food Board, Rosie Boycott, said she hoped the scheme would be introduced in the capital in 2014.
"With the pilot store in Barnsley testing the model to ensure it's sustainable, the London Food Board is looking forward to helping establish stores across London in the New Year," she said.
- The Daily Mail
