Nicola Probert is nervous. She hasn't let her partner, Tony Hodge, go food shopping for the family on his own since the day he came back with a £3 DVD, a six-pack of premium baked beans and two milkshakes for the children – an extra £10 on the bill that meant their two sons couldn't go to the soft play centre that weekend. Today, though, Nicola has no choice: she is recovering from a minor operation and can't leave the house. She isn't happy.

"Please don't get Heinz baked beans," she implores him, handing over the shopping list she's written out in painstaking detail. "Even if they're on offer, they're more expensive than own-brand. Don't get posh, individual packets of crisps either; get the supermarket ones that come in multipacks. And please don't buy any of those offers they pile up by the front door of the supermarket – they're always more expensive than the stuff you can find at the back of the shop."

Tony sighs. Nicola tries to make amends. "We can afford some fresh meat this week," she coaxes. Then pausing, adds: "As long as they've got their three-for-£10 deal still going." The couple exchange a look of exasperation, then burst into exhausted laughter. Nicola, however, stops after a couple of seconds. "Sometimes I wonder what's happened to our family," she says sadly. "It's not like we're the poorest of the poor. A few years ago, we didn't have to count the pennies like this."

Nicola is a phlebotomist, taking blood samples from patients, on maternity leave after the birth of the couple's second child seven months ago. Tony works full-time in the building trade. The couple live in Bristol on a household income of around £24,500 a year. They spend around £80 on food every two weeks. "We don't have trouble keeping to our budget in other areas – although with fuel bills rocketing up, we're fortunate our flat is a heat trap – but when it comes to food, it's a constant struggle just to buy enough food to fill our stomachs," says Nicola.

"It makes me furious. Affordable, nutritious food should be a right for everyone, not a privilege for a few."

The couple are among the more than 13 million people who live in poverty in the UK, suffering what the Joseph Rowntree Trust says are food shortages on a scale not seen since wartime rationing. Food prices have spiked across the world but in Britain, where we import around 40% of our food, prices have risen at more than twice the EU average and families are struggling to afford food that has increased by 32% since 2007.

"Many people don't think that in the UK – the seventh richest country in the world – people go hungry or go hungry for healthy food," said Lindsay Boswell, chief executive of FareShare, the UK charity that feeds 36,500 people every day, redistributing high-quality, surplus food from the food industry to a network of community organisations that support vulnerable people across Britain. "But they do. Many families are feeling the pinch financially as a result of unemployment and redundancies, the high cost of living and government spending cuts." Research is building up, pointing to the fact that people on what were once regarded as reasonable salaries can no longer afford to eat enough, much less eat enough healthy food. A recent report by Save the Children looked at 5,000 families with incomes of up to £30,000 a year and found that to ensure their children get enough food to eat, nearly two-thirds of parents skip meals, go into debt, avoid paying bills, and put off replacing worn-out clothing.

Giselle Cory, a senior research and policy analyst at the Resolution Foundation, says families on £42,500 are struggling and those on £50,000 could be next to discover they are no longer able to afford the food they want. "We're very much not only talking about society's poorest," she said. "We're talking about families who, a short while ago, could afford their weekly shop without a problem. These are the ones who are now struggling to get by."

Two children in every school class are going hungry because their parents fail to provide proper meals, according to a study by the parenting website Netmums and the child welfare charity Kids Company, with an estimated one million children in the UK now living in homes without enough to eat. A Guardian teacher network survey in June found that four out of five teachers (83%) saw pupils hungry in the morning and 55% said up to a quarter arrived having not eaten enough. Almost half of teachers had brought food in for pupils who arrived at school with empty stomachs.

Most experts agree the problem of Britain's nutritional recession is going to get worse, with the cost of the weekly shop continuing to rise by about 4% a year until 2022 at least, an increase almost twice the current rate of inflation of 2.7%. The average cost of a food shopping bill in Britain is £76.83 a week, an increase of £5.66 compared with last year, according to Which?. In a decade, the annual food bill for the average family will be over £4,000, up from £2,766 last year.

In Bristol, where the Hodges live, a recent report by Oxfam revealed that 26,500 people can't afford to eat enough. At least one in every 16 parents say they skip one meal a week so their family doesn't go hungry, with 41% saying they have been "forced" to buy cheaper food because healthy food has become unaffordable.

Emma Murray, co-founder of the Bristol North West Food Bank, has seen an increasing number of professional people arrive at her door, needing emergency food parcels. "We don't just get unemployed council house families here by any means," she said. "We had a gentleman here last week who lived in Clifton, the most affluent part of Bristol. He had lost his job and was mortified to find himself asking for our help. We had another professional woman the other day who was so embarrassed to be here that she couldn't come through the door."

Murray's food bank has fed over 3,000 people since it opened 20 months ago, many referred from agencies, including GPs, health visitors, schools and job centres. "There's a lot of disbelief about food poverty because families who have always been able to afford to live independently of the state are very ashamed about needing help for something as essential as food," she said.

At the supermarket, Tony heads to the Branson's baked beans piled up by the front door, £1.50 for three tins. "Last week, these were £1 for four," he says. "It's disgusting the way supermarkets try to squeeze extra money from families who are struggling and can't afford the extra pennies, even with something as small as a tin of beans." He makes his way down the aisles, gazing blankly from side to side. "Food doesn't mean anything nice to me any more. It just makes me feel stressed," he says. "The cheap things we can afford are so tasteless and pointless that I often can't even be bothered to eat."

Carefully choosing a small onion and a single floret of broccoli, he glances over at the peppers. "My oldest boy loves peppers. It's the one healthy food he can't get enough of," he says. "But look at the price of them. We'd have to go without a meal just so that he can have a healthy snack."

It takes Tony five minutes to scour the shelves for the cheapest jam. "To be honest, I wouldn't be this careful if I wasn't being watched, but it means I've saved myself about £2 on jam and the same on baked beans," he says. "I'm itching to buy something that actually tastes nice and would be a treat but Nicola would go mad, and she'd be right to." As he heads to the till, however, he grabs two Cornish pasties, on offer at two for £1. "Nicola won't like that," he says. "But I have to leave the house at 5am every morning and sometimes I forget to make lunch – or we don't have enough food in for me to do it.

"It's bad to buy those pasties, I know, but it's less bad than if I have to buy something at work, where it'll cost four times as much."

Both the Department of Health (DoH) and the British Retail Consortium (BRC), the trade association representing retailers from large supermarkets to independent shops, insist that families can eat both healthily and cheaply. According to government estimates, poor households could eat within the official Eatwell healthy eating guidelines if they spent just 21p more on food each week. The Department for Environment, Food and Rural Affairs (Defra) estimates that low-income households spend £16.49 per person each week on foods in the Eatwell categories. But, the department says, they could meet all the Eatwell goals by increasing their spend on food to £16.70 and spending £2.77 a week less on high-fat/high-sugar foods, £1.88 more on bread and other starchy foods and £2.22 more on fruit and vegetables.Prof Philip James, a former nutrition adviser to the government and president of the International Association for the Study of Obesity, rejects these claims.

"The reality is that anyone who does not essentially live independently of any state influence – that is, those who have no mortgage, whose salary has not been frozen and who have a handsome pension – is going to be affected by a government making some of the biggest cuts to local authority budgets at the same time that it is predicted food prices are going to rise even further," he said.

Healthy eating is expensive – and increasingly so, according to research by Mysupermarket.co.uk, the price comparison and shopping site, which shows that, in the past year alone, staples such as 500g of minced beef have risen by a fifth, from £2.20 to £2.80, while a 1kg bag of onions is up by 18%, from 87p to £1.02. Carrots, potatoes, eggs and orange juice have also seen steep rises. Although processed food has seen the sharpest price rise – 36% – since 2007, the next steepest rise, at 34%, has been in fruit. The cost of vegetables has risen by 22% over the same period.

The government assessment of food affordability paints a bleak picture of how the diet of the nation's poorest 10% has deteriorated since the financial crash. Between 2007 and 2010, the most recent period analysed, low-income households cut the amount of food they buy by 11%. But while trading down to cheaper products has helped many people offset some of the food price rises, low-income households have not managed to trade down, possibly because they were already buying cheaper products, the report suggests.

In 2010, the poorest 10% bought 26% less red meat and pork than in 2007, 25% less fruit and 15% less vegetables, raising concerns that the food industry and the government are not doing enough to promote affordable, healthy food choices for all segments of society. This, says Cory, corresponds to what Resolution sees on the ground. "It's unequivocal," she said. "When food prices go up and household incomes go down, people on low to middle incomes buy less healthy food and more unhealthy food. It's a very real causation and, frankly, an unarguable one."

Back in Bristol, Nicola is unpacking Tony's shopping bags as he hovers anxiously. "You've done well," she says finally. "This was a big shop and I was expecting it to cost £50 and you've come in at £46.19, even with those pasties."

Tony peers over her shoulder to try to identify something he wants to eat for supper. There isn't anything. He slumps down on the sofa and reaches for the remote control.

"It just all looks so cheap and nasty," he says. "To be honest, just looking at it takes my appetite away."

• This article was amended on 20 November 2012. The original said that in 2010, the poorest 10% bought 26% less fresh meat than in 2007. That has been corrected to red meat and pork. An estimate that low-income households spend £16.49 per person each week on foods in the Eatwell categories was by Defra, not the Department of Health; and research about the rising cost of staple foods was by Mysupermarket.co.uk, not the government's Food Statistics Pocketbook. These points have been corrected.