Tucked away on the New King’s Road in Fulham, west London, there is a delicatessen called Bayley & Sage. It’s the stuff of foodie fantasy: heaps of purple artichokes spill over piles of grooved and polished heritage tomatoes the colour of a newly painted post box. It suits the neighbourhood, with its infestation of four-by-four baby buggies, macchiato-sipping au pairs and tree-lined streets of neatly appointed red brick villas. This is not a place of want. Surely nobody here can be in need?

Then again, this is 21st-century Britain, and here plenty and hunger sit far too comfortably side by side. Just a few minutes’ walk away on Studdridge Street is Christ Church. To aficionados of the decorative arts it is famous for its glorious stained glass windows by Edward Burne-Jones; to those with hungry mouths to feed, it is better known for the food bank that operates here on Friday afternoons. The tomatoes they hand out won’t be heritage but canned.

“The area does look affluent,” agrees Daphine Aikens, who has run the operation for three years and is just one of the thousands of volunteers in this country now helping to operate food banks. “But we’re surrounded by social housing and people come to us from all over the borough.” This food bank is one of 350 run nationwide by the church-based charity the Trussell Trust, which is opening them at the rate of three a week. It operates on a voucher system. To get a parcel of three days’ free food, applicants must first be referred by a recognised agency: the local jobcentre, for example, the Citizens Advice Bureau or their GP, which hands out the vouchers. Under the trust’s rules, nobody can have more than three vouchers in a row. The charity says it wants to provide breathing space for those in acute need, rather than become a solution to a chronic problem.

Aikens is seeing many more people coming to her door with those vouchers. In the second quarter of this year, she says, they saw a 250% increase compared to the same period last year. Her own experience is backed up by nationwide research. A report, co-written by Oxfam and Church Action on Poverty, that was released in May found that 500,000 people in Britain had resorted to food banks to feed themselves this year, three times more than in the previous 12 months. Campaigners are certain they know why it’s happening. The complex calculus of modern living and expenditure is no longer adding up.

Between 2000 and 2011, food prices rose by 43%, while general prices rose by 28% and incomes stagnated or even fell. If you’re on a low income, food price rises have simply been amplified. On top of that have come draconian changes to the benefits rules, combined with infuriating administrative incompetency.

“The government shies away from the truth of just how much trouble a bureaucratic welfare system can cause,” says Chris Mould, chief executive of the Trussell Trust. He says his charity is meant to provide a safety net, “but it’s hard to hold that line as an organisation working in support of the state, rather than becoming a substitute for it”. He is unapologetic about the trust’s Christian motives. “We are motivated by the challenge Jesus gave to his followers,” he says. “We do this because we should, and not in a trade-off with the state.” Sadly, the state doesn’t appear to be listening. As far as they’re concerned, it’s fine for churches to fill in the yawning gaps.

Chris Johns, director of Oxfam’s UK Poverty Programme, is even more explicit. The need for food banks is being caused not just by changing benefits provision, but also by the way government agencies temporarily remove benefits for perceived misdemeanours: a failure to sign the right paperwork, or apply for the right training scheme. Then, having stopped their benefits so they can’t buy food, the same agency gives claimants a food bank voucher. “They are being given the vouchers by the people who are sanctioning them. It’s almost beyond description,” Johns says. “Food banks are clearly fitting into a hole left by the welfare state.”

Not that the government will acknowledge this. Last month, the work and pensions minister Lord Freud, a former investment banker, said that it was not possible to make a connection between changes to benefits rules and a rise in demand for food banks. “Food banks are absolutely not part of the welfare system that we run,” he said. “We have other systems to support people.” The real issue, he said, is the provision of free stuff. “Clearly food from a food bank is by definition free and there’s almost infinite demand.” And all this despite the fact that it is agencies run by the DWP – jobcentres – which are recognising the need by handing out the vouchers.

Challenged on this, a spokesperson for the DWP pointed out that “referrals from jobcentres only make up a very small proportion of overall numbers”.

The stream of people arriving at Christ Church with a voucher just need food. A week ago this food bank staged a collection outside a major local supermarket and amassed three tonnes of the stuff. Supermarket customers buy the food they donate; the supermarket then gives the charity a shopping voucher of their own, equivalent to a third of the food’s value, so they are not profiting from the donations. As a result the shelves, in a back room dominated by the famed stained glass windows, are full. There is no refrigeration, so along with tinned food there are bags of pasta and jars of sauces, and other basics such as shampoo, and nappies for those with kids.

Aikens admits that coming to a place like this is not easy for many. “People are reticent,” she says. “We give the food freely but they have to be prepared to walk over the threshold and say I need help.” Does she ever despair at the problems people get themselves into? “I constantly say that we mustn’t be judgmental. I think a place like this is about the basic imperative of caring. A civilised society cares about its most vulnerable members.”

Waiting quietly at a table in the reception area is Debra Lonergan, mother of three teenage boys, who is also her husband’s full-time carer. The benefits agency has told her that they have just noticed she was overpaid £600 back in 2009 so they are stopping her money for a month. “I’ve been telling them I’d know if I’d received an extra £600,” she says, desperately. “I don’t owe them anything.” She is working to get the problem sorted, but for now she has a practical issue. There’s not enough food in the house to keep the kids fed. Her GP gave her the Trussell Trust voucher. “This is my first time at a food bank. It’s daunting. I didn’t know what to expect. I had the image of queuing up Russian style, but it wasn’t like that.” Instead, each applicant sits down with a volunteer who offers them a cup of tea and goes through that list of exactly what they need. Debra tells me she wants to work, is desperate to, but that home circumstances just make it impossible.

Jacquie Bunce says the same. She has been signed off as unfit to work because of serious depression. Her benefits were stopped after she failed to turn up for a medical she says she was too unwell to attend. “I need to work,” she says. “I want to work.” But she just can’t find employment. “Everyone’s embarrassed about coming here,” she says, looking around the room. “I’m not happy to be here. And if I was working and could give to the food bank I would.” Instead she finds herself needing to take. “The government are happy to let it happen. They’re not in touch with the real world.” Jacquie is well dressed, wears her jewellery with pride. She acknowledges this. “Of course some people cheat the system. There are always people like that. But don’t look down on someone because they’ve got a big telly. They may have had all that before they found themselves out of work.”

Aikens agrees. People are quick to make assumptions. She has given talks in fee-paying schools and recognised kids in the assemblies, whose family have sought help from the food bank. “Maybe the kids have a scholarship for the fees but there’s no money at home for food,” she says. “We have a number of people who come here who are in full-time work but they just don’t have enough.”

I travel north from the manicured streets of Fulham to a light industrial estate on the outskirts of Hull, and the warehouses that are home to the non-denominational charity Real Aid. It started here in 2001 with a focus on development work in places like Sierra Leone, but in 2007 the floods in Hull made them realise there was need closer to home. “We were seeing people in our own community living in poverty,” says the charity’s director, Lindsay Killick. So now, as well as working abroad, they run an operation gathering in food, and distributing it to other organisations in East Yorkshire and Humberside.

They also run a food bank in nearby Bridlington aimed specifically at working families. “Working families find it harder to come and ask for help,” Killick says. “Generally, they’ve not been in this situation before.” The solution: they charge a small fee for the food. “Charging £1.50 can make it easier.” For that they may get upwards of £15 worth of food, but it feels less like charity and more like an equitable exchange. It gives the lie to Lord Freud’s claim of a “something for nothing” culture.

Killick shows me round the warehouse, stacked with pallets of food liberated from supermarkets and producers. They have a local farmer who sends them half a tonne of potatoes every week, a donation worth £250. Other stuff comes from Asda’s national distribution centre in Wakefield. In all they shift around 400 tonnes of food a year. Not that getting hold of it is always easy. Big players like the Trussell Trust or the waste food charity FareShare have access to some of the biggest supplies. It seems the food bank world is becoming crowded. “It’s not so much competition as protectionism. We’ll approach a company for donations and they’ll say they’re already giving to another organisation.” He tells me that a supermarket where they once did a collection received a complaint from a much larger charity which thought that was their pitch.

What about demand? “We have a waiting list for groups and community centres wanting to join the schemes.” And that demand is only increasing. In April, responsibility for crisis loan funds moved from the DWP to local authorities. The local authority in their area then drew up a list of “partners” to whom people in need could be referred, if they didn’t qualify for a loan. “We’re now on that list,” Killick says. “We weren’t asked to be on that list. We just get people turning up saying the council told me to come down here.”

I travel with the Real Aid delivery van to Unity in the Community, a bustling centre in Orchard Park, a district of Hull which has seen better days. Low-rise social housing is punctuated by 60s tower blocks marked for demolition. This area is one of the most deprived in Britain. Volunteers help unload bags of fruit and vegetables, catering tins of tuna and ravioli and beans, and separate them out into equal parcels.

“We don’t use vouchers here,” says Dennis Woods, who runs the centre. “We don’t want personal information. We don’t want to put them in a difficult position.” They just have to hand over £1.50. And if they don’t have it? He takes a deep breath. “We sort them out.” Nobody in need leaves empty-handed. The centre also provides training in skills such as IT to help people get back to work, advice on benefit entitlements and many other things. As in Fulham, the growth area here is the working poor.

I meet grandmother Ann Jones, a tidy, self-contained woman, who is waiting patiently in the reception area for her bags, which she will unload into a shopping trolley. “I come here for my daughter. She works full-time as a carer. She went to university, worked hard. But with rent at £550 and school dinners costing £80 it’s just hard to make ends meet.” Ann says she doesn’t like doing this, says it’s an embarrassment. “I’ve worked hard all my life. You’re 65 years old and coming in for a bag of food. I was ashamed. But at the end of the day we all need a bit of help.” Her bags have arrived and she takes me through what she’s been given. There’s a huge can of tuna. “You can do a lot with that. Tuna pasta, fishcakes, tuna bake. Sometimes there’s flour so I make cakes with that.” Is the cost of meat a problem? “Of course it bloody is. Everything’s a problem.”

There are pensioners here, who have worked all their lives and now can’t manage on what income they have. “My state pension only pays the rent,” says Ann Fleming. “This is a really useful service because it’s basic and healthy things. And I don’t feel so bad about taking it because you’re paying £1.50.” Alan Martin has been using the service since it opened. “In this world we should not have to rely on things like this but we do.”

It takes a couple of hours, but soon the 35 or so parcels of food are gone. There is, of course, a familiar rhetoric that surrounds all this: a narrative in which a robust welfare state merely gets people addicted to benefits and handouts, and that a food bank is just handouts in protein and carbs. We can argue about the validity of that argument, and politicians and experts from all parts of the spectrum often do. But anyone travelling across the landscape of food banks in Britain today, as I have, will quickly come to the same conclusion. This isn’t just about problems with a broken benefits system, however acute they may be. It’s also about working people who have tried their best to make ends meet. It is about people who believe in paying their way but who are now so unable to do so they need free food.