Falling incomes and welfare spending cuts have triggered an explosion in demand for emergency food parcels as Britain's poorest families struggle to put a meal on the table, say charities.

FareShare, a charity that supplies millions of free meals to charities, food banks and breakfast clubs using food donated by supermarkets, said it could not keep pace with demand, which it expected to continue growing for at least five years.

"We are experiencing ridiculous growth. The only brake is how much food we can get out of the industry. We have the operational capacity to deliver more food and the charities that want to take that food," said Lindsay Boswell, chief executive of FareShare.

FareShare said the food it distributed in 2011-12 contributed to more than 8.6m meals, benefiting an average 36,500 people a day via 720 organisations that deal with people in food poverty. Its long-term plans are to triple the numbers of people and charities it supplies. Along with charity shops and payday loans companies, food banks have become one of recession Britain's high growth sectors. Originally set up to support homeless individuals, food banks report they increasingly serve families hit by benefit cuts or unemployment, and low-income working households who can't make ends meet.

The Guardian's Breadline Britain investigation revealed last week that up to 3.6m UK households were at risk of slipping into poverty as a result of spiralling living costs, shrinking incomes and welfare benefit reforms. Britain's biggest food-bank network, the Trussell Trust charity, reported in April it had doubled the number of emergency food parcels issued over the past year and was opening food banks at the rate of two a week.

Chris Mould, director of the Trussell Trust, said: "Every day we meet parents who are skipping meals to feed their children or even considering stealing to stop their children going to bed hungry. It is shocking that there is such a great need for food banks in 21st-century Britain, but the need is growing."

Foodbanks are thriving not just in Britain's most deprived areas but in some of its wealthiest areas, like Poole in Dorset. The seaside town boasts some of Britain's most expensive property but in April its local foodbank supplied food parcels to nearly 300 people – more than twice as many as in April 2010, with the extra demand driven by low income working families

The shadow environment minister, Mary Creagh, whose brief covers food poverty, said the growth in emergency food distribution was a sign that the government's austerity measures were hurting ordinary families: "It's a disgrace that in the seventh richest country in the world we have people queuing for food handouts, and this is only going to get worse."

FareShare said that in 2001 nearly 42% of the charities it supplied had reported a "substantial increase" in demand for food, and that four out of 10 said their budgets had been reduced by public spending cuts. It had seen a 40% increase in demand for food from breakfast clubs, which supply free early-morning meals to underprivileged children.

Boswell said FareShare had even been informally approached by an NHS trust hospital to see if it would supply it. Boswell, who would not name the trust, said: "They were literally just trying to see if there was a way they could cut their food bills. I said no, for obvious reasons."

Boswell said: "Every piece of evidence we have got is that demand will only increase over time as more people lose their jobs and living costs go up. Even if the economy improves there will be a considerable lag before that trickles through to individuals who use the services the charities support. We are forecasting that we will see growth for at least the next five years." FareShare estimates it could provide 70m free meals if just 1% of the estimated 3m tonnes of food fit for consumption "wasted" each year in the UK by the food industry was rescued. It works with successfully with companies like Sainsbury's and Nestle, but says it needs more companies to come on board.

The government said it was committed to helping households on low incomes. A Department for Work and Pensions spokesman said the benefits system provided a safety net for people who need it to cover costs such as food and housing, and emergency financial support through crisis loans. He said that the rise in demand for emergency food parcels reflected ministers' decision to allow jobcentre advisers to issue claimants facing benefits delays with vouchers redeemable at Trussell Trust food banks. The DWP said it did not keep a record of how many vouchers had been issued.

The trust, which operates 201 UK food banks on a franchise basis, reported l in April that it had fed 128,000 people over the past year, distributing 1,225 tonnes of food donated by the public, schools and businesses. It estimates that half a million people a year will be in receipt of a food parcel by 2016, by which time it aims to have opened 500 food banks. The Salvation Army, whose churches issue food parcels on an informal basis, said its biggest distribution point, in Keighley, West Yorkshire, was so inundated this year it had to temporarily restrict food parcels to people referred by local charities and health professionals.

A spokesman for the Child Poverty Action Group said: "It's clear that this is an early-warning indicator of how bad things are starting to get for poorer families and how bad things are going to get in future. This should be setting alarm bells ringing for the government."

Food banks: how you can help

• There are hundreds of foodbanks in towns and cities across the UK, providing free food parcels for thousands of families and individuals each week. Most are run locally, operating through churches, faith organisations and community groups, sometimes as small independent charities.

• The public can help in three ways: by donating food, money or volunteer time, according to the Trussell Trust, which oversees a network of 200 local food banks across the UK.

• Food banks will normally accept all non-perishable food. "As a general rule our banks tend to run low on things like sugar, long-life milk and pasta sauce. You may not automatically think of things like this but they make such a difference," said a Trussell spokesman.

• Each bank will have its own specific food requirements, so contact your local branch for details. Branches will also have details of collection points, sometimes held outside supermarkets, where shoppers are asked on their way in if they would buy items from a specific list prepared by the local food bank.

• People can also donate money towards the running costs of local food banks, or volunteer: most food banks need people to help with the collection, storage, packing, sorting and distribution of food parcels.

• The Guardian is crowdsourcing a directory of UK foodbanks. Please add details of your local bank to our interactive online map