By the time most visitors reach the doors of Hammersmith and Fulham Foodbank in London, they have not eaten properly for several days. This church hall, where volunteers from the Trussell Trust hand out emergency food, could pass for David Cameron's "big society" incarnate.

The hungry who come here must be referred by a recognised public authority – it might be a school that has noticed children are not being fed, a GP who has noticed signs of malnutrition, or a social worker who finds a mental health patient is not eating. The food that is distributed is not state welfare but donated by the public. The network of women who do Cameron's heavy lifting are unpaid local Christians who are unfailingly caring and sensitive. The Trussell Trust has seen a huge surge in demand for centres like this around the country since the recession; it fed 41,000 people in 2009-10 and expects to feed over 100,000 in 2011-12. More and more, it is helping people who are in work but struggling with stagnant wages, and soaring food and fuel bills.

The daily experience of hunger is reappearing in Britain, one of the world's richest countries. Behind the undoubtedly good private work to relieve it is a public moral failure.

The H&F foodbank is located in one of those streets that have become enclaves of stratospheric City wealth in the last three decades. They are intensely relaxed about being filthy rich here – Chelsea tractors on parade outside £2m-£3m 19th-century red-brick villas, home cinemas displayed in immaculate architectural extensions of sheet glass. Next door to the foodbank is the Hurlingham clinic, where the elite's need for expensive physical perfection can be met with "aesthetic procedures" from injectable fillers to cellulite management.

The inequalities that have been allowed to emerge in this one street are so stark they recall an era as long past as the period of its houses. The emergence of need like this alongside such affluence requires not just philanthropic intervention but confronting at both ends of the income scale – as Labour's shadow secretary of state for the environment and food, Mary Creagh, said in a debate on food poverty last week.

The coalition has plunged into welfare reforms that will increase hunger, with benefits increases calculated on lower measures of inflation than previously – despite soaring rates affecting essentials such as food and fuel. It has also launched an attack on wages for those at the bottom of the scale, with the national minimum wage out of kilter with living costs, proposals to allow regional variations in the minimum wage that would cut it further, and the abolition of the Agricultural Wages Board, which set living standards for many rural workers in the lowest paid jobs. Yet it has left high pay untouched and, in the case of the top 1% with offshore trusts, lightly taxed. Its rhetoric on capping benefits so that recipients should not be better off than the average working family casts poverty once more in the 18th-century language of Malthus, which saw hunger as a necessary spur to the idle to work.

Daphine Aikens, H&F foodbank's manager, ran through the reasons her visitors find themselves unable to eat: 22% are on incomes so low, in work or on benefits, that the smallest upset tips them into crisis; 10% have had their benefits reassessed and can no longer make ends meet; 8% have fallen into debt, often as a result of soaring energy bills, or transport costs; 7% are recently unemployed and delays in benefit claims have left them temporarily destitute.

The foodbanks increasingly come across unemployed young adults on benefit payments of around £53 a week, even though the Rowntree Trust calculates that the minimum required to buy a basic healthy diet alone is £46 a week.

One afternoon last week, I watched the parcels go out. Audrey, shedding tears of shame, had given most of her pension cheque to her daughter and grandchildren following a fire that destroyed their home. The daughter, a single parent and pharmacist – retraining as a teacher so she could look after the children in the holidays – had not been able to afford insurance, so had been left with nothing. Audrey was having the grandchildren for the weekend but had no money to feed them. She had been living on a diet of breakfast cereal and crackers with small bits of cheese.

João, from Portugal, had been fully employed in low-paid catering jobs since 2004 but was made redundant this year. He fell into debt because he was not allowed to escape his mobile phone contract. He had applied for the two vacancies at the jobcentre that morning, but they had gone. He had been going two to three days at a time without food, going to bed to conserve energy. How could hunger spur him to greater efforts to work when there are no jobs?

A pregnant mother with two children and no food for their supper, husband at work, too distressed to talk; a young man with mental health problems, moved from a hostel to a flat and waiting for his benefits to be transferred, no food for nearly three days and no money for heating ... the litany of hardship is humbling. The archaic attitude that this sort of hunger is individual failure rather the experience of victims of circumstance, or often of a capricious economic system beyond their control, was abandoned well over a century ago. Let's not go back to it now.

Some of the names in this article have been changed.